causality will be broken in at least one frame -- time moving backwards is inherently reversing the properties of the event.
i don't have issues conceiving of things moving faster than light locally. but the things that do cannot carry info (for instance entanglement of quantum particles).
The notion of causality gets bent a little, but not broken. Time in the preferred frame becomes the preferred measure of past and future, for ordering one's sense of causality. Again, consider that the lack of loops in the preferred frame can't be contorted into loops in any frame.
Now, if you don't agree with my notion of a "loop" being necessary to create a paradox, that's another matter.
Causality isn't broken because even when, in a non-preferred frame, an effect would seem to precede its own cause, there's always a space-like interval between anomalously ordered events.
In terms of what you might literally see, that is observe happening in the world around after waiting for light from such events to reach your eye, you wouldn't ever see anything out of the ordinary. You would always see an effect come after its cause, and you would only arrive at the weirdness of measuring that an effect came "first" by compensating for light delay, by computing time coordinates of cause and effect events within your own frame.
As I said lack of causality or even misordering of causality is break of the first axiom of relativity -- the basic idea that physical properties are the same in all frames. A loop is not the paradox -- if any connectivity is broken in any frame relativity fails. If you could get something to move FTL then the info it carries would be giberish.
As I said lack of causality or even misordering of causality is break of the first axiom of relativity -- the basic idea that physical properties are the same in all frames. A loop is not the paradox -- if any connectivity is broken in any frame relativity fails. If you could get something to move FTL then the info it carries would be giberish.
In case you didn't notice, I'm casually tossing aside the idea that physical properties are the same in all frames. From the beginning, I said that this FTL hack was against the spirit of relativity. Whether it's a fictitious must-be-one-of-a-kind magical lattice that sends FTL signal, or an only somewhat less whimsical "hyperaether" which can transmit FTL signals, I do not deny the idea that there would be introduced new physical properties of the universe that would measure differently in different frames.
The question is, does this FTL concept run contrary to currently measured confirmations of relativity, or merely to a higher notion of frame-of-reference egalitarianism, which inspired the development of relativity, but might not actually have to be true in order to get the results we've gotten so far from what relativity predicts.
you can always throw in more properties, the problem is there seems to be a requirement that properties are the same in all frames. sure we can throw away relativity but what good does it do? the replacement theory has to cover the properties observed within relativity. there is also a truism and perhaps at some point a law which states that nature acts with the least number of assumptions, making a specific frame in which only one property is observed is adding unnecessary complexity -- theory follows observation and there have been no observations of anything with regard to the hypothetical universe you propose.
While it would be cool if ftl signals were possible, the same as it would be cool if i could move objects with my mind, you toss aside relativity with too much easy.
you can always throw in more properties, the problem is there seems to be a requirement that properties are the same in all frames.
"Seems to be a requirement" in what sense? What actually breaks by introducing a preferred frame, other than the "purity" of the idea of relativity? Does something utterly break, does an equation suddenly divide by zero or tell you 3 = 5?
Relativity is a good guiding principle -- I don't argue with that. One should be suspicious of anything that violates the principle that all physical properties will measure the same in all frames of reference. A lot of insight was gained by adopting the relativity principle, and measurements of known phenomena have fit as predicted into that framework.
Regardless, you can overstate relativity's case. Einstein did not disprove the existance of something like the aether, he merely made it arbitrary and superfluous. It's not that the aether didn't work or couldn't exist, but that any aether in any arbitrary frame of reference would work, and you wouldn't be able to measure it. If the laws of physics would conspire to make the aether totally undetectable, why even bother to suppose it's there at all?
But now I'm proposing (for sake of argument -- not because I think it's really there!) an kind of aether that would be detectable if it existed. Detecting it would involve discovering some kind of informating-bearing FTL phenomena that allows non-local causality. Obviously, we've never encountered such a thing, and may never do so.
My only concern here is "With the right set of rules, with the right set of tricky loopholes, is non-paradoxical, information-bearing FTL that produces non-local cause-and-effect relationships even imaginable in a world where relativity (with a small "r") is also true?"
By "relativity with a small 'r'" I mean a Minkowskian spacetime geometry, known non-FTL phenomena in accord with Einstein's relativity, but allowing for the philosophical bias toward total equivalence of all reference frames to be bent as needed.
the thing is that you arent saying anything. What do you mean by preferred frame of reference? How exactly will having one allow FTL communication?
Until you define preferred frame of reference, I cannot say how the theory responds to that mathematical entry.
And if by prefered frame of reference you mean the only frame in which FTL communication can occur, you have your break right there -- FTL communication needs to be able to occur in a frames or else relativity is broken.
You are right about the aether -- Michealson-Morley experiment disproved the existence of the aether before Einstein.
Edit: and there is no such thing as non-local (ie global?) causality -- this is from GR.
the thing is that you arent saying anything. What do you mean by preferred frame of reference?
The message-sending lattice we talked about is an example of a preferred frame. After using that idea of a fanciful physical artifact to get the thought experiment going, substitute the fictional one-of-a-kind artifact with an "aether", which has a frame of reference which can be defined by the way its hypothetical ability to transmit FTL information operates.
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How exactly will having one allow FTL communication?
I'm not saying that having a preferred frame of reference causes FTL phenomena to spring into being. I'm saying that, starting with the presumption that FTL communication exists, anchoring the time flow of those messages to always be forward in time within one special preferred frame helps get you around paradoxical outcomes.
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Until you define preferred frame of reference, I cannot say how the theory responds to that mathematical entry.
The preferred frame is defined as the frame in which all FTL message are guaranteed to move forward in time, the frame in which a message sent at time t will arrive no sooner than t + epsilon, where epsilon is an arbitralily small positive value. By definition, the behavior of these FTL messages is plainly, clearly, undeniably and deliberately not in tune with relativity. This is the starting point for further speculation.
If you treat that starting point as if it's the very definition of the ending point, we'll obviously not get anywhere.
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And if by prefered frame of reference you mean the only frame in which FTL communication can occur, you have your break right there -- FTL communication needs to be able to occur in a frames or else relativity is broken.
Must... not... lose... patience... grrrrrrr...
How many times and in how many different ways do I have to say that I KNOW that making any frame of reference preferred goes against what's normally meant by relativity???
My point is that, I think with the right tricks, you can keep the outcomes predicted by relativity insofar as known phenomena are concerned, still use the same math for those phenomena, yet imagine information-bearing FTL communication that doesn't cause causality paradoxes, like sending yourself a message telling yourself not to send yourself a message.
FTL communication would be able to occur in other frames of reference... I'm not setting any weird hypothetical restriction such having to come to rest in the preferred frame before you're allowed to send a message. But only in one frame are you guaranteed that messages will always go forward in time. In all other frames, it's possible to send messages backward in time.
Again, if you immediately yell "paradox! that's broken!" the moment you hear the idea of an information-bearing signal going backward in time, we'll not get anywhere. My premise is that it takes more than information going backward in time to cause a paradox. It takes a closed loop of information-bearing signals or actions, where a chain of events can close back on itself, to cause a paradox.
A mere one-way sending of information backward in time doesn't in-and-of itself created such a loop. I believe that a preferred-frame kludge prevents such a loop from forming.
If you can send a message backward in time, how do you avoid causality problems? It works out that if a message goes back in time one year, that the message can only be received somewhere at least one light year away. As a consequence of FTL messages always moving forward in time in the preferred frame, I can't send a message backward in time one year to a place that's only a mile away.
A return message can't get to me sooner than my outgoing message because, moving the other way "against the aether", the return message will take at least a year to get to me.
As a practical matter, round-trip communication to distant places would be essentially instantaneous regardless of your frame of reference, regardless of your motion relative to the aether.
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You are right about the aether -- Michealson-Morley experiment disproved the existence of the aether before Einstein.
MM failed to find an aether, but only disproved one particular notion of it. There were ways to rescue the aether, but only by the self-defeating modifications to the concept that made would save the aether while making it impossible to detect at the same time. Why have a theory about something you can't by definition ever test?
Don't get too hung up on the original idea of the aether... I'm partly using the word "aether" as a quaint homage to the past. My aether is not for the tranmission of light, but for the transmission of FTL signals. It does share in the idea of being a medium that permeates all space, and it would represent its own intertial reference frame. It would be detectable, therefore not a difference that makes no difference.
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Edit: and there is no such thing as non-local (ie global?) causality -- this is from GR.
And yes, the Earth is not flat. I see that looking at the globe on my desk and looking it up in the encyclopedia. Definitions and assumptions are being bent and tweaked here. The question is do SR and GR completely break down under the assumption of non-local causality -- not free-form non-local causality, but a causality with a new set of constraints -- faster than light being possible, but always moving forward in time within one special frame of reference.
Simple proof. Time moves forward in all frames (true? -- it is a universal assumption in all science). Forward time is defined by increased entropy. The amount of information in a system can be defined by its entropy (this 'can be' has been shown to mean that entropy is fully equivalent to information). Information cannot be sent backwards because that would itself be a decrease in information (entropy) of the universe of some future point going against all sorts of laws that have nothing to do with relativity.
Think of this as a conservation of mass issue -- something has to come from the past to the present at the same time (that is precisely instantaneously) that we try to send stuff backwards.
(I believe the above requirements causes a causality loop)
With your assumptions of FTL, you have to ignore the issue of forward time and the fact that in all frames the entropy of the universe should be the same. You are not merely talking about the property of FTL being special, you are saying that the frame in which FTL is found is special in more ways than just allowing FTL to exist nonparadoxically. This is a frame in which none of the laws of the universe are known to apply, not even the direction of forward time. It is an intriguing construction but utterly useless for individuals who live outside of it -- is there even information in the FTL frame?
Simple proof. Time moves forward in all frames (true? -- it is a universal assumption in all science). Forward time is defined by increased entropy. The amount of information in a system can be defined by its entropy (this 'can be' has been shown to mean that entropy is fully equivalent to information). Information cannot be sent backwards because that would itself be a decrease in information (entropy) of the universe of some future point going against all sorts of laws that have nothing to do with relativity.
At least now we're getting somewhere more interesting than "You're violating relativity because you're violating relativity."
Einstein's physics violated Newtonian conservation of energy. Einstein created a new conservation of energy by creating the idea of mass/energy equivalence, specifically by equating the rest mass of an object to a specific amount of energy -- the famous E=mc^2.
This kind of FTL already starts playing with how time is defined anyway, because time in the preferred frame would become the most important measure of time. In that frame, nothing goes backward in time. Backwardness in time in other frames can be measured, but it's a very academic backward motion in time since it's always non-local.
If that sounds a bit dismissive, consider this real-world consequence of how time is defined under relativity: Say a billion years from now, a star in a galaxy a billion light years away is seen, from telescopes on Earth, exploding from into a supernova. One could say that the star is exploding right now, but that we won't see the event for a billion years because of how long it takes for light to reach us.
Remember, however, that the notion of simultaneity, of "right now" is relative to a frame of reference, and that even small changes in velocity change your reference frame. You can almost think about a frame of reference "pivoting" around an object as it changes velocity, and the three-dimension slice of four-dimensional space-time called "now" for that object sweeps through difference slices of space time as the object changes velocity. The greater the distance between you and an event, the greater the effect a small change in your velocity makes in how you would notate the time coordinates of that event, just like when you swing a long pole the end that's far away from you moves much farther than the part of the pole near your body.
Merely by walking around in my room I can swing the moment of the star's explosion around in time. If the star is exploding "now" while I'm standing still, I take a step away from the star, and now it exploded a few years ago in my new reference frame. Turn around and walk towards star, and in this third reference frame, the star won't explore for a few more years.
This is all very academic, however, because this strange fluctuating dating of the event can only happen once I really know that the event has occurred, around a billion years from now.
So, yes, my FTL scheme violates a full relativistic sense of entropy, but only in the same sense that I'm really changing when a star explodes by walking around in my room. Entropy would be perfecting preserved within the preferred frame of reference, and go more and more out of whack as your velocity relative to the preferred frame increases, but even then, the violation of entropy would be non-local, sealed off from you at a safe distance.
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Think of this as a conservation of mass issue -- something has to come from the past to the present at the same time (that is precisely instantaneously) that we try to send stuff backwards.
(I believe the above requirements causes a causality loop)
I don't see a loop here, just a non-local violation of entropy as discussed above. The violation would have to "catch up" with its precipitating event to cause a loop, and it can't do so as far as I can see.
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It is an intriguing construction but utterly useless for individuals who live outside of it -- is there even information in the FTL frame?
Go back to the original image of the lattice of clocks, adding to each clock a little data terminal where you can pick up and receive messages sent along the lattice from any clock to all other clocks. Further, suppose you can use these data terminals by radio control, so you don't have to physically stop relative to the lattice to use one of the terminals, but can even pick up and drop off message while flying by at high speed.
Living "outside the frame of reference" of the lattice doesn't mean the lattice is hidden or inaccessible to you, all it means is that you are moving relative to the lattice. You can send a message to a distant friend while remaining in motion by sending it to your nearest lattice terminal, she can pick the message up from her nearest terminal while also in motion, and similarly draft a response and return it to you.
The lattice remains quite useful to you, even though you aren't in its frame of reference. The important thing in communication is round-trip message time, and even for people moving relative to the lattice, round-trip message times can be arbitrarily close to instantaneous. Sent in one particular direction along the lattice, a message might take a whole year to get where it's going, but the return message will be able to go backward in time nearly a year, so the benefit if instantaneous round-trip communication is preserved.
I don't think you understand my entropy argument -- the entropy of the universe is something you can "measure" at any time; it increases in all frames as time goes forward -- yet in all frames it is the same at any point. If it appears that information is sent back in time in one frame -- which is to say that the entropy of the universe has decreased (which is a violation of physical properties outside of relativity but we will go with it) -- then the measurement of the entropy of the universe in all frames will necessarily be less than it was in the previous time it was measured causing the violation to be true in all frames. There is no preferred frame in which this is not true. Hence you cannot send information backwards in time even if it appears that it goes back in time in only one frame.
If you want FTL signaling you will need to do it in a frame which is not a part of the universe -- meaning it cannot receive information from the universe since it is necessarily decoupled from the measurement of entropy in order for FTL signaling to actually occur (it would be like a rip in time -- but since it is a frame and not an actual event it would be a "subspace" heh.). What this effectively means is that our universe cannot do anything to the FTL subspace -- we cannot send signals through it, etc etc.
The loop of causality is a two body loop -- the minimal size necessary -- the future event is as necessary as the past event.
I don't think you understand my entropy argument -- the entropy of the universe is something you can "measure" at any time; it increases in all frames as time goes forward -- yet in all frames it is the same at any point.
You're right... I don't understand what you're saying here.
I understand that entropy is supposed to increase going forward in time. That I know.
I understand that entropy should increase in all frames. I'm willing to tweak the rules for sake of argument that the preferred frame is the only frame where entropy always increases, but that's another matter.
What I don't get is what you mean by "yet in all frames it is the same at any point". Entropy is the same at any point in time? In space?
I'd have to know more about how "the entropy of the universe" is defined as a measurable property to make more sense of this. I find myself thinking about the exploding star I mentioned earlier -- clearly, a star blowing up represents a major increase in entropy. Yet just by walking around my room, I can place such an increase of entropy into my past, present, or future.
Since I doubt that such small local motions are supposed to affect what's meant by the measured entropy of the universe, I'd be inclined to think that the proper measure is somehow related to the local circumstances of the one doing the measuring, and if that's the case, sending information back into time non-locally shouldn't cause any problems.
The total entropy in the universe is "measurable" in the sense that it could be measured but not easily. What I mean when I say it is the same in all frames is that irrespective of the motion of a frame, the total entropy measured at a given moment in time (this is not looking at the stars and counting some measure of entropy but in essence "measuring" entropy at every point in the universe at one time) should be identical to the total entropy measured at the same point in another frame moving at some different velocity.
The total entropy in the universe is "measurable" in the sense that it could be measured but not easily. What I mean when I say it is the same in all frames is that irrespective of the motion of a frame, the total entropy measured at a given moment in time (this is not looking at the stars and counting some measure of entropy but in essence "measuring" entropy at every point in the universe at one time) should be identical to the total entropy measured at the same point in another frame moving at some different velocity.
If entropy is always increasing, then the measure of entropy is time dependant.
Time is relative across frames, so you can't say the total entropy in the universe in one frame is the same as it is in another frame "at the same time", because there is no such thing as "at the same time" (except for "at the same time and place").
At any rate, I'm not seeing any troubling violations of causality yet -- and by "troubling" I mean leading to a clear paradox.
I'm the one with the crackpot hypothetical idea, so I know that the burden of proof is on me, but if you'll humor me, I'd like to see if you can follow my rules (as best you understand them) and come up with a shoot-your-own-grandpa type of paradox that I can't prevent by my rules. This would include problems with entropy that lead to clear local violations of entropy, like seeing the (absolute) future or running a machine off its own waste heat or something like that.
shetline, the total entropy of the universe is a physical property of the universe. while it increasing does define forward time, it does not have a set law saying it increases at a certain rate with time, so it is not time dependent as such -- it defines forward time. There is a concept of same time in relativity, an event that begins in one frame and ends some time later will appear (when considering the speed of the signal) to begin at the same time and end at the same time in another frame (the time the event takes to occur will of course vary in the two frames but the beginning and ending of the event occurs identically -- this allows interconversion between frames of reference, if this were not true then well none of this would matter). You can measure entropy in two frames at the same time and they should read the same number because it is a universal property. In other words, think of the universe as a adiabatic box on your lab bench, you measure the entropy of the contents of the box and that value should be identical to that of someone who measured the value of the same box at the same time but while driving by at 0.5c.
I am trying to convince you without using relativity (other than fundamental properties remain the same in all frames) that a signal that appears to go back in time in one frame is thermodynamically impossible in all frames.
By showing you this, I hope I can make you realize that a frame in which FTL signalling is allowed is essentially a frame that is not in contact with our universe.
I can show you a paradox simply. Deterministic physics is not a full description of what occurs (ie there is chaos). In order for me to send a signal backwards in time (in any frame), I need to obtain at least the amount of entropy i send back back from the place I sent. This requires all events between the past and the future to be fully determined such that any and all information that signal carries is identical, which we know is not observed let alone theoretically possible.
Local violations of entropy are allowed, btw. The machine example is an adiabatic system, ie its a minature mock up of the way the universe works.
There is a concept of same time in relativity, an event that begins in one frame and ends some time later will appear (when considering the speed of the signal) to begin at the same time and end at the same time in another frame (the time the event takes to occur will of course vary in the two frames but the beginning and ending of the event occurs identically -- this allows interconversion between frames of reference, if this were not true then well none of this would matter).
Conversion of time coordinates between frames is something that I know reasonably well, and what you've said above makes no sense.
An event in frame A starts at time ta_0 (damn the lack of subscripts and superscripts in vB code!), and ends at time ta_1, taking a duration da. It follows that...
ta_1 = ta_0 + da
In other words, the end time equals the start time plus the duration.
You're telling me that the duration in frame B can be different from frame B (which is correct -- time dialation), but that after allowing for light travel time, the start time and end time in both frames will be the same. Therefore...
tb_0 = ta_0
tb_1 = ta_1
db != da
tb_1 = ta_0 + da = ta_0 + db, where da != db???
How can the start and end times of an (extended) event be the same when the duration in between the start and the end times is different? (The reason I added the parenthetical "extended" is because the typical use of the word "event" is for a single point in space time of zero duration.)
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I can show you a paradox simply. Deterministic physics is not a full description of what occurs (ie there is chaos). In order for me to send a signal backwards in time (in any frame), I need to obtain at least the amount of entropy i send back back from the place I sent.
I don't think you're getting what I mean by a paradox. I mean something like "This statement is a lie", where the logic runs in self-contradictory circles.
Breaking the standard definition of entropy is not to be taken lightly, but it's not a paradox. As far as I can tell so far, time defined by increasing entropy survives my FTL scheme -- with a little modification. It doesn't break down in a "man who shaves all men who do not shave themselves" heap of inconsistencies.
I'm also not sure you're getting what I mean when I say that nothing goes backward in time in the preferred frame, but things can go backward in other frames. I'm beginning to get the impression that you're coming from the other direction and saying "If something goes backward in a non-preferred frame, it sure as hell can be seen as going backward in the preferred frame, unless you put that preferred frame in a separate universe." If that's where you are, then I've got some more explaining to do, because that's not how what I'm trying to describe works.
I'm not saying that willy-nilly, anyone in a non-preferred frame can wildly send information back in time however they like, just because they aren't in the preferred frame. The only backwardness I'm allowing comes from translating forward-marching, preferred frame FTL events into time coordinates of other frames. The backwardness seen from doing such event coordinate translations is the only backward-through-time causality that my FTL rules allow.
By definition, no sending of information, no causal event, runs backward in the preferred frame. As long as that condition holds, then at the very least entropy always increases in the preferred frame.
you are right -- you just dont get what i am saying.
If I am looking at an experiment happening in another moving frame, I and i was able to talk to a person in that frame we would both agree that the event started and stoped at the same time -- not t=5.2 s after midnight, but the same time (remember there is no absolute scale). The duration of the event would be different in both frames but the point at which it began and ended would be the same.
I understand completely your argument, and you are simply wrong. Uncoupling your frame is necessary for your argument to work, ANY percieved backwards in time motion causes the entropy of the universe to decrease in all frames because it has to be the same in all frames. This a violation of thermo.
Its not that the rules of the universe simply apply to all frames, its that all frames are intrinsically coupled causing the rules of the universe to apply to all frames. Basically I am getting a sense that you dont understand the premise behind my first paragraph in this post. The observed events are the same in relativity -- their space time durations differ in different frames, but they are the same.
Fundamentally, if something appears to go back in time in any frame, it cannot occur. Period. This can be shown through several other theories, but I choose thermo because its relatively easy to argue and you werent accepting relativistic arguments.
You cannot have a special frame in which events occur that arent observed in other frames. That is relativity. You cannot send stuff back in time because that causes a decrease in the universe's entropy. That is thermo.
Your condescension is not unexpected due to my confusion with the whole setting the clocks argument, but it is unwarented, I assure you. I am not the first to make these arguments and you are no doubt not the first to think you can make a special frame that has special properties. You dont understand what a frame is -- it is merely an observation point -- it doesnt change the properties of the universe; certain frames make CALCULATIONS easier but the same CALCULATIONS can be done in other frames.
Thinking a frame is a special place is sweet, really, but its not.
You cannot have a special frame in which events occur that arent observed in other frames.
When or where did I ever say that events in the preferred frame couldn't be observed in any other frame?
Think back to the clock lattice with its FTL data terminals... The lattice would be "out there", floating around in space, and anyone in any frame of reference can look at, fly up to and touch it, stare at the clocks through a telescope while flying by in a different frame of reference, send and received messages sent through the lattice, again while in motion relative to the latice, and hence in a different frame. Of course it?s observable ? it wouldn?t be very useful if it were invisible!
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Thinking a frame is a special place is sweet, really, but its not.
Again, consider the example above. I'm not calling the preferred frame a "special place". The only meaning of the preferred frame is that, if you plot out a sequence of FTL events, when you look at events translated into coordinates for that frame, cause always precedes effect, send always precedes receive. When you send a message from one place along the lattice to another, the message isn't allowed to show up until the next arbitrarily small forward tick of all of the synchronized clocks in the lattice.
sorry not events. i meant physical property. frames cannot hold properties yet you clearly indicated that in the prefered frame FTL signalling was possible. you cannot do that. the properties are intrinsic to the universe not to the frames used to observe them.
that lattice work of clocks is a teaching tool. its great that you have your construct based around it, but it doesnt show that you have any understanding of what einstein was getting at. you cant give frames physical properties. just having a frame in which something is possible (like it doesnt appear to go back in time) doesnt mean the event is possible, there is a paradox intrinsic to the fact that you are just using a frame to measure a property and the event must be the same regardless of frames. Toss away relativity and you still have the problems with thermo etc etc. There is something intrinsic to the fact that nothing can go back in time.
sorry not events. i meant physical property. frames cannot hold properties yet you clearly indicated that in the prefered frame FTL signalling was possible. you cannot do that. the properties are intrinsic to the universe not to the frames used to observe them.
Didn't I say that I knew I was violating the frame-egalitarianism of relativity from the start? That's the premise... break the rules a little, see how far things get out of hand. Do I break only a bit of philosophy, do I produce consequences that runs counter to things that have actually been measured (and I don't think anyone has every actually measured the total entropy of the universe), do I create an internal contradiction in the special rules I propose?
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that lattice work of clocks is a teaching tool. its great that you have your construct based around it, but it doesnt show that you have any understanding of what einstein was getting at. you cant give frames physical properties.
You can't, or else... what? That's the whole point of the hypothetical exercise. Break that rule, in a very particular, careful way, and see what happens.
It would be kind of a pointless exercise if all I was asking is which rules can I break without breaking any rules.
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just having a frame in which something is possible (like it doesnt appear to go back in time) doesnt mean the event is possible
Again, I'm not saying the rule causes such an event to be possible. The game is merely to ask, if FTL is possible, and it follows these particular non-relativistic rules, what happens?
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there is a paradox intrinsic to the fact that you are just using a frame to measure a property and the event must be the same regardless of frames.
That's a simple contradiction, not a paradox. I'm deliberately contradicting the assumption that everything has to be the same across all frame, to see what the contradiction buys me, and what's left of what we'd normally expect.
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Toss away relativity and you still have the problems with thermo etc etc. There is something intrinsic to the fact that nothing can go back in time.
First of all, I'm not tossing relativity completely away... I'm keeping time dilation, the light-speed limit for all information-bearing interactions other than the special FTL messages, a Minkowskian spacetime geometry, etc.
I'm mostly keeping the idea that nothing can go backward in time. Nothing can go backward in time in the preferred frame, and in other frames, all backwardness is non-local.
Here's a painfully forced analogy for what I'm trying to do... Consider three proposals for changing the rules of baseball.
1) Replace the baseballs with oranges.
2) You aren't allowed to hit the ball.
3) Pitchers must bat for all team members, and only those team member, who don't bat for themselves.
Given Proposal 1, you could just dig in your heels and say "Well, if you don't use baseballs, it isn't baseball anymore, is it?" and stop there.
Or you could explore the idea, "Well, it would certainly be a messier game. I don't know if the outfielders would have much to do anymore, since it'd be hard to hit an orange very far. Say, can we freeze the oranges? Etc., etc." The game would be quite a bit different, but something still recognizably baseball would survive. Things wouldn't be so broken that you couldn't discuss consequences.
Given Proposal 2, with no options given for something else you're allowed to do instead of hit the ball, it's pretty clear that you?d outright kill the game off with the rule change. All players could do is stand there until they strike out, and no one would ever score.
Proposal 3 doesn't merely break the game, it leads to a logical paradox in which you can't define whether or not the pitcher must or must not bat for himself.
For my FTL proposal, I want to see if it can at least hold up on a Proposal 1 kind of level.
Comments
Originally posted by billybobsky
causality will be broken in at least one frame -- time moving backwards is inherently reversing the properties of the event.
i don't have issues conceiving of things moving faster than light locally. but the things that do cannot carry info (for instance entanglement of quantum particles).
The notion of causality gets bent a little, but not broken. Time in the preferred frame becomes the preferred measure of past and future, for ordering one's sense of causality. Again, consider that the lack of loops in the preferred frame can't be contorted into loops in any frame.
Now, if you don't agree with my notion of a "loop" being necessary to create a paradox, that's another matter.
Causality isn't broken because even when, in a non-preferred frame, an effect would seem to precede its own cause, there's always a space-like interval between anomalously ordered events.
In terms of what you might literally see, that is observe happening in the world around after waiting for light from such events to reach your eye, you wouldn't ever see anything out of the ordinary. You would always see an effect come after its cause, and you would only arrive at the weirdness of measuring that an effect came "first" by compensating for light delay, by computing time coordinates of cause and effect events within your own frame.
Originally posted by billybobsky
As I said lack of causality or even misordering of causality is break of the first axiom of relativity -- the basic idea that physical properties are the same in all frames. A loop is not the paradox -- if any connectivity is broken in any frame relativity fails. If you could get something to move FTL then the info it carries would be giberish.
In case you didn't notice, I'm casually tossing aside the idea that physical properties are the same in all frames. From the beginning, I said that this FTL hack was against the spirit of relativity. Whether it's a fictitious must-be-one-of-a-kind magical lattice that sends FTL signal, or an only somewhat less whimsical "hyperaether" which can transmit FTL signals, I do not deny the idea that there would be introduced new physical properties of the universe that would measure differently in different frames.
The question is, does this FTL concept run contrary to currently measured confirmations of relativity, or merely to a higher notion of frame-of-reference egalitarianism, which inspired the development of relativity, but might not actually have to be true in order to get the results we've gotten so far from what relativity predicts.
While it would be cool if ftl signals were possible, the same as it would be cool if i could move objects with my mind, you toss aside relativity with too much easy.
Originally posted by billybobsky
you can always throw in more properties, the problem is there seems to be a requirement that properties are the same in all frames.
"Seems to be a requirement" in what sense? What actually breaks by introducing a preferred frame, other than the "purity" of the idea of relativity? Does something utterly break, does an equation suddenly divide by zero or tell you 3 = 5?
Relativity is a good guiding principle -- I don't argue with that. One should be suspicious of anything that violates the principle that all physical properties will measure the same in all frames of reference. A lot of insight was gained by adopting the relativity principle, and measurements of known phenomena have fit as predicted into that framework.
Regardless, you can overstate relativity's case. Einstein did not disprove the existance of something like the aether, he merely made it arbitrary and superfluous. It's not that the aether didn't work or couldn't exist, but that any aether in any arbitrary frame of reference would work, and you wouldn't be able to measure it. If the laws of physics would conspire to make the aether totally undetectable, why even bother to suppose it's there at all?
But now I'm proposing (for sake of argument -- not because I think it's really there!) an kind of aether that would be detectable if it existed. Detecting it would involve discovering some kind of informating-bearing FTL phenomena that allows non-local causality. Obviously, we've never encountered such a thing, and may never do so.
My only concern here is "With the right set of rules, with the right set of tricky loopholes, is non-paradoxical, information-bearing FTL that produces non-local cause-and-effect relationships even imaginable in a world where relativity (with a small "r") is also true?"
By "relativity with a small 'r'" I mean a Minkowskian spacetime geometry, known non-FTL phenomena in accord with Einstein's relativity, but allowing for the philosophical bias toward total equivalence of all reference frames to be bent as needed.
Until you define preferred frame of reference, I cannot say how the theory responds to that mathematical entry.
And if by prefered frame of reference you mean the only frame in which FTL communication can occur, you have your break right there -- FTL communication needs to be able to occur in a frames or else relativity is broken.
You are right about the aether -- Michealson-Morley experiment disproved the existence of the aether before Einstein.
Edit: and there is no such thing as non-local (ie global?) causality -- this is from GR.
Originally posted by billybobsky
the thing is that you arent saying anything. What do you mean by preferred frame of reference?
The message-sending lattice we talked about is an example of a preferred frame. After using that idea of a fanciful physical artifact to get the thought experiment going, substitute the fictional one-of-a-kind artifact with an "aether", which has a frame of reference which can be defined by the way its hypothetical ability to transmit FTL information operates.
How exactly will having one allow FTL communication?
I'm not saying that having a preferred frame of reference causes FTL phenomena to spring into being. I'm saying that, starting with the presumption that FTL communication exists, anchoring the time flow of those messages to always be forward in time within one special preferred frame helps get you around paradoxical outcomes.
Until you define preferred frame of reference, I cannot say how the theory responds to that mathematical entry.
The preferred frame is defined as the frame in which all FTL message are guaranteed to move forward in time, the frame in which a message sent at time t will arrive no sooner than t + epsilon, where epsilon is an arbitralily small positive value. By definition, the behavior of these FTL messages is plainly, clearly, undeniably and deliberately not in tune with relativity. This is the starting point for further speculation.
If you treat that starting point as if it's the very definition of the ending point, we'll obviously not get anywhere.
And if by prefered frame of reference you mean the only frame in which FTL communication can occur, you have your break right there -- FTL communication needs to be able to occur in a frames or else relativity is broken.
Must... not... lose... patience... grrrrrrr...
How many times and in how many different ways do I have to say that I KNOW that making any frame of reference preferred goes against what's normally meant by relativity???
My point is that, I think with the right tricks, you can keep the outcomes predicted by relativity insofar as known phenomena are concerned, still use the same math for those phenomena, yet imagine information-bearing FTL communication that doesn't cause causality paradoxes, like sending yourself a message telling yourself not to send yourself a message.
FTL communication would be able to occur in other frames of reference... I'm not setting any weird hypothetical restriction such having to come to rest in the preferred frame before you're allowed to send a message. But only in one frame are you guaranteed that messages will always go forward in time. In all other frames, it's possible to send messages backward in time.
Again, if you immediately yell "paradox! that's broken!" the moment you hear the idea of an information-bearing signal going backward in time, we'll not get anywhere. My premise is that it takes more than information going backward in time to cause a paradox. It takes a closed loop of information-bearing signals or actions, where a chain of events can close back on itself, to cause a paradox.
A mere one-way sending of information backward in time doesn't in-and-of itself created such a loop. I believe that a preferred-frame kludge prevents such a loop from forming.
If you can send a message backward in time, how do you avoid causality problems? It works out that if a message goes back in time one year, that the message can only be received somewhere at least one light year away. As a consequence of FTL messages always moving forward in time in the preferred frame, I can't send a message backward in time one year to a place that's only a mile away.
A return message can't get to me sooner than my outgoing message because, moving the other way "against the aether", the return message will take at least a year to get to me.
As a practical matter, round-trip communication to distant places would be essentially instantaneous regardless of your frame of reference, regardless of your motion relative to the aether.
You are right about the aether -- Michealson-Morley experiment disproved the existence of the aether before Einstein.
MM failed to find an aether, but only disproved one particular notion of it. There were ways to rescue the aether, but only by the self-defeating modifications to the concept that made would save the aether while making it impossible to detect at the same time. Why have a theory about something you can't by definition ever test?
Don't get too hung up on the original idea of the aether... I'm partly using the word "aether" as a quaint homage to the past. My aether is not for the tranmission of light, but for the transmission of FTL signals. It does share in the idea of being a medium that permeates all space, and it would represent its own intertial reference frame. It would be detectable, therefore not a difference that makes no difference.
Edit: and there is no such thing as non-local (ie global?) causality -- this is from GR.
And yes, the Earth is not flat. I see that looking at the globe on my desk and looking it up in the encyclopedia. Definitions and assumptions are being bent and tweaked here. The question is do SR and GR completely break down under the assumption of non-local causality -- not free-form non-local causality, but a causality with a new set of constraints -- faster than light being possible, but always moving forward in time within one special frame of reference.
maybe some links will help...
NASA links on quantum entanglement
Queensland University research
New Scientist magazine - downplaying time travel, leaning in on quantum entanglement for cryptography
Nauture Magazine trumpets a "Trillion-atom triumph" in entangled physics
WIRED comments on the Danish entanglement research
still searching for the link to a story last year or two claiming actual success,
not sure if it was via Bose-Einstein Condensate (slowing light) or independent of the BEC medium
<returns to dig through archived links>
Simple proof. Time moves forward in all frames (true? -- it is a universal assumption in all science). Forward time is defined by increased entropy. The amount of information in a system can be defined by its entropy (this 'can be' has been shown to mean that entropy is fully equivalent to information). Information cannot be sent backwards because that would itself be a decrease in information (entropy) of the universe of some future point going against all sorts of laws that have nothing to do with relativity.
Think of this as a conservation of mass issue -- something has to come from the past to the present at the same time (that is precisely instantaneously) that we try to send stuff backwards.
(I believe the above requirements causes a causality loop)
With your assumptions of FTL, you have to ignore the issue of forward time and the fact that in all frames the entropy of the universe should be the same. You are not merely talking about the property of FTL being special, you are saying that the frame in which FTL is found is special in more ways than just allowing FTL to exist nonparadoxically. This is a frame in which none of the laws of the universe are known to apply, not even the direction of forward time. It is an intriguing construction but utterly useless for individuals who live outside of it -- is there even information in the FTL frame?
Originally posted by billybobsky
You are killing me shetline.
Simple proof. Time moves forward in all frames (true? -- it is a universal assumption in all science). Forward time is defined by increased entropy. The amount of information in a system can be defined by its entropy (this 'can be' has been shown to mean that entropy is fully equivalent to information). Information cannot be sent backwards because that would itself be a decrease in information (entropy) of the universe of some future point going against all sorts of laws that have nothing to do with relativity.
At least now we're getting somewhere more interesting than "You're violating relativity because you're violating relativity."
Einstein's physics violated Newtonian conservation of energy. Einstein created a new conservation of energy by creating the idea of mass/energy equivalence, specifically by equating the rest mass of an object to a specific amount of energy -- the famous E=mc^2.
This kind of FTL already starts playing with how time is defined anyway, because time in the preferred frame would become the most important measure of time. In that frame, nothing goes backward in time. Backwardness in time in other frames can be measured, but it's a very academic backward motion in time since it's always non-local.
If that sounds a bit dismissive, consider this real-world consequence of how time is defined under relativity: Say a billion years from now, a star in a galaxy a billion light years away is seen, from telescopes on Earth, exploding from into a supernova. One could say that the star is exploding right now, but that we won't see the event for a billion years because of how long it takes for light to reach us.
Remember, however, that the notion of simultaneity, of "right now" is relative to a frame of reference, and that even small changes in velocity change your reference frame. You can almost think about a frame of reference "pivoting" around an object as it changes velocity, and the three-dimension slice of four-dimensional space-time called "now" for that object sweeps through difference slices of space time as the object changes velocity. The greater the distance between you and an event, the greater the effect a small change in your velocity makes in how you would notate the time coordinates of that event, just like when you swing a long pole the end that's far away from you moves much farther than the part of the pole near your body.
Merely by walking around in my room I can swing the moment of the star's explosion around in time. If the star is exploding "now" while I'm standing still, I take a step away from the star, and now it exploded a few years ago in my new reference frame. Turn around and walk towards star, and in this third reference frame, the star won't explore for a few more years.
This is all very academic, however, because this strange fluctuating dating of the event can only happen once I really know that the event has occurred, around a billion years from now.
So, yes, my FTL scheme violates a full relativistic sense of entropy, but only in the same sense that I'm really changing when a star explodes by walking around in my room. Entropy would be perfecting preserved within the preferred frame of reference, and go more and more out of whack as your velocity relative to the preferred frame increases, but even then, the violation of entropy would be non-local, sealed off from you at a safe distance.
Think of this as a conservation of mass issue -- something has to come from the past to the present at the same time (that is precisely instantaneously) that we try to send stuff backwards.
(I believe the above requirements causes a causality loop)
I don't see a loop here, just a non-local violation of entropy as discussed above. The violation would have to "catch up" with its precipitating event to cause a loop, and it can't do so as far as I can see.
It is an intriguing construction but utterly useless for individuals who live outside of it -- is there even information in the FTL frame?
Go back to the original image of the lattice of clocks, adding to each clock a little data terminal where you can pick up and receive messages sent along the lattice from any clock to all other clocks. Further, suppose you can use these data terminals by radio control, so you don't have to physically stop relative to the lattice to use one of the terminals, but can even pick up and drop off message while flying by at high speed.
Living "outside the frame of reference" of the lattice doesn't mean the lattice is hidden or inaccessible to you, all it means is that you are moving relative to the lattice. You can send a message to a distant friend while remaining in motion by sending it to your nearest lattice terminal, she can pick the message up from her nearest terminal while also in motion, and similarly draft a response and return it to you.
The lattice remains quite useful to you, even though you aren't in its frame of reference. The important thing in communication is round-trip message time, and even for people moving relative to the lattice, round-trip message times can be arbitrarily close to instantaneous. Sent in one particular direction along the lattice, a message might take a whole year to get where it's going, but the return message will be able to go backward in time nearly a year, so the benefit if instantaneous round-trip communication is preserved.
If you want FTL signaling you will need to do it in a frame which is not a part of the universe -- meaning it cannot receive information from the universe since it is necessarily decoupled from the measurement of entropy in order for FTL signaling to actually occur (it would be like a rip in time -- but since it is a frame and not an actual event it would be a "subspace" heh.). What this effectively means is that our universe cannot do anything to the FTL subspace -- we cannot send signals through it, etc etc.
The loop of causality is a two body loop -- the minimal size necessary -- the future event is as necessary as the past event.
Originally posted by billybobsky
I don't think you understand my entropy argument -- the entropy of the universe is something you can "measure" at any time; it increases in all frames as time goes forward -- yet in all frames it is the same at any point.
You're right... I don't understand what you're saying here.
I understand that entropy is supposed to increase going forward in time. That I know.
I understand that entropy should increase in all frames. I'm willing to tweak the rules for sake of argument that the preferred frame is the only frame where entropy always increases, but that's another matter.
What I don't get is what you mean by "yet in all frames it is the same at any point". Entropy is the same at any point in time? In space?
I'd have to know more about how "the entropy of the universe" is defined as a measurable property to make more sense of this. I find myself thinking about the exploding star I mentioned earlier -- clearly, a star blowing up represents a major increase in entropy. Yet just by walking around my room, I can place such an increase of entropy into my past, present, or future.
Since I doubt that such small local motions are supposed to affect what's meant by the measured entropy of the universe, I'd be inclined to think that the proper measure is somehow related to the local circumstances of the one doing the measuring, and if that's the case, sending information back into time non-locally shouldn't cause any problems.
Originally posted by billybobsky
The total entropy in the universe is "measurable" in the sense that it could be measured but not easily. What I mean when I say it is the same in all frames is that irrespective of the motion of a frame, the total entropy measured at a given moment in time (this is not looking at the stars and counting some measure of entropy but in essence "measuring" entropy at every point in the universe at one time) should be identical to the total entropy measured at the same point in another frame moving at some different velocity.
If entropy is always increasing, then the measure of entropy is time dependant.
Time is relative across frames, so you can't say the total entropy in the universe in one frame is the same as it is in another frame "at the same time", because there is no such thing as "at the same time" (except for "at the same time and place").
At any rate, I'm not seeing any troubling violations of causality yet -- and by "troubling" I mean leading to a clear paradox.
I'm the one with the crackpot hypothetical idea, so I know that the burden of proof is on me, but if you'll humor me, I'd like to see if you can follow my rules (as best you understand them) and come up with a shoot-your-own-grandpa type of paradox that I can't prevent by my rules. This would include problems with entropy that lead to clear local violations of entropy, like seeing the (absolute) future or running a machine off its own waste heat or something like that.
I am trying to convince you without using relativity (other than fundamental properties remain the same in all frames) that a signal that appears to go back in time in one frame is thermodynamically impossible in all frames.
By showing you this, I hope I can make you realize that a frame in which FTL signalling is allowed is essentially a frame that is not in contact with our universe.
I can show you a paradox simply. Deterministic physics is not a full description of what occurs (ie there is chaos). In order for me to send a signal backwards in time (in any frame), I need to obtain at least the amount of entropy i send back back from the place I sent. This requires all events between the past and the future to be fully determined such that any and all information that signal carries is identical, which we know is not observed let alone theoretically possible.
Local violations of entropy are allowed, btw. The machine example is an adiabatic system, ie its a minature mock up of the way the universe works.
Originally posted by billybobsky
There is a concept of same time in relativity, an event that begins in one frame and ends some time later will appear (when considering the speed of the signal) to begin at the same time and end at the same time in another frame (the time the event takes to occur will of course vary in the two frames but the beginning and ending of the event occurs identically -- this allows interconversion between frames of reference, if this were not true then well none of this would matter).
Conversion of time coordinates between frames is something that I know reasonably well, and what you've said above makes no sense.
An event in frame A starts at time ta_0 (damn the lack of subscripts and superscripts in vB code!), and ends at time ta_1, taking a duration da. It follows that...
ta_1 = ta_0 + da
In other words, the end time equals the start time plus the duration.
You're telling me that the duration in frame B can be different from frame B (which is correct -- time dialation), but that after allowing for light travel time, the start time and end time in both frames will be the same. Therefore...
tb_0 = ta_0
tb_1 = ta_1
db != da
tb_1 = ta_0 + da = ta_0 + db, where da != db???
How can the start and end times of an (extended) event be the same when the duration in between the start and the end times is different? (The reason I added the parenthetical "extended" is because the typical use of the word "event" is for a single point in space time of zero duration.)
I can show you a paradox simply. Deterministic physics is not a full description of what occurs (ie there is chaos). In order for me to send a signal backwards in time (in any frame), I need to obtain at least the amount of entropy i send back back from the place I sent.
I don't think you're getting what I mean by a paradox. I mean something like "This statement is a lie", where the logic runs in self-contradictory circles.
Breaking the standard definition of entropy is not to be taken lightly, but it's not a paradox. As far as I can tell so far, time defined by increasing entropy survives my FTL scheme -- with a little modification. It doesn't break down in a "man who shaves all men who do not shave themselves" heap of inconsistencies.
I'm also not sure you're getting what I mean when I say that nothing goes backward in time in the preferred frame, but things can go backward in other frames. I'm beginning to get the impression that you're coming from the other direction and saying "If something goes backward in a non-preferred frame, it sure as hell can be seen as going backward in the preferred frame, unless you put that preferred frame in a separate universe." If that's where you are, then I've got some more explaining to do, because that's not how what I'm trying to describe works.
I'm not saying that willy-nilly, anyone in a non-preferred frame can wildly send information back in time however they like, just because they aren't in the preferred frame. The only backwardness I'm allowing comes from translating forward-marching, preferred frame FTL events into time coordinates of other frames. The backwardness seen from doing such event coordinate translations is the only backward-through-time causality that my FTL rules allow.
By definition, no sending of information, no causal event, runs backward in the preferred frame. As long as that condition holds, then at the very least entropy always increases in the preferred frame.
If I am looking at an experiment happening in another moving frame, I and i was able to talk to a person in that frame we would both agree that the event started and stoped at the same time -- not t=5.2 s after midnight, but the same time (remember there is no absolute scale). The duration of the event would be different in both frames but the point at which it began and ended would be the same.
I understand completely your argument, and you are simply wrong. Uncoupling your frame is necessary for your argument to work, ANY percieved backwards in time motion causes the entropy of the universe to decrease in all frames because it has to be the same in all frames. This a violation of thermo.
Its not that the rules of the universe simply apply to all frames, its that all frames are intrinsically coupled causing the rules of the universe to apply to all frames. Basically I am getting a sense that you dont understand the premise behind my first paragraph in this post. The observed events are the same in relativity -- their space time durations differ in different frames, but they are the same.
Fundamentally, if something appears to go back in time in any frame, it cannot occur. Period. This can be shown through several other theories, but I choose thermo because its relatively easy to argue and you werent accepting relativistic arguments.
You cannot have a special frame in which events occur that arent observed in other frames. That is relativity. You cannot send stuff back in time because that causes a decrease in the universe's entropy. That is thermo.
Your condescension is not unexpected due to my confusion with the whole setting the clocks argument, but it is unwarented, I assure you. I am not the first to make these arguments and you are no doubt not the first to think you can make a special frame that has special properties. You dont understand what a frame is -- it is merely an observation point -- it doesnt change the properties of the universe; certain frames make CALCULATIONS easier but the same CALCULATIONS can be done in other frames.
Thinking a frame is a special place is sweet, really, but its not.
Originally posted by billybobsky
You cannot have a special frame in which events occur that arent observed in other frames.
When or where did I ever say that events in the preferred frame couldn't be observed in any other frame?
Think back to the clock lattice with its FTL data terminals... The lattice would be "out there", floating around in space, and anyone in any frame of reference can look at, fly up to and touch it, stare at the clocks through a telescope while flying by in a different frame of reference, send and received messages sent through the lattice, again while in motion relative to the latice, and hence in a different frame. Of course it?s observable ? it wouldn?t be very useful if it were invisible!
Thinking a frame is a special place is sweet, really, but its not.
Again, consider the example above. I'm not calling the preferred frame a "special place". The only meaning of the preferred frame is that, if you plot out a sequence of FTL events, when you look at events translated into coordinates for that frame, cause always precedes effect, send always precedes receive. When you send a message from one place along the lattice to another, the message isn't allowed to show up until the next arbitrarily small forward tick of all of the synchronized clocks in the lattice.
that lattice work of clocks is a teaching tool. its great that you have your construct based around it, but it doesnt show that you have any understanding of what einstein was getting at. you cant give frames physical properties. just having a frame in which something is possible (like it doesnt appear to go back in time) doesnt mean the event is possible, there is a paradox intrinsic to the fact that you are just using a frame to measure a property and the event must be the same regardless of frames. Toss away relativity and you still have the problems with thermo etc etc. There is something intrinsic to the fact that nothing can go back in time.
Originally posted by billybobsky
sorry not events. i meant physical property. frames cannot hold properties yet you clearly indicated that in the prefered frame FTL signalling was possible. you cannot do that. the properties are intrinsic to the universe not to the frames used to observe them.
Didn't I say that I knew I was violating the frame-egalitarianism of relativity from the start? That's the premise... break the rules a little, see how far things get out of hand. Do I break only a bit of philosophy, do I produce consequences that runs counter to things that have actually been measured (and I don't think anyone has every actually measured the total entropy of the universe), do I create an internal contradiction in the special rules I propose?
that lattice work of clocks is a teaching tool. its great that you have your construct based around it, but it doesnt show that you have any understanding of what einstein was getting at. you cant give frames physical properties.
You can't, or else... what? That's the whole point of the hypothetical exercise. Break that rule, in a very particular, careful way, and see what happens.
It would be kind of a pointless exercise if all I was asking is which rules can I break without breaking any rules.
just having a frame in which something is possible (like it doesnt appear to go back in time) doesnt mean the event is possible
Again, I'm not saying the rule causes such an event to be possible. The game is merely to ask, if FTL is possible, and it follows these particular non-relativistic rules, what happens?
there is a paradox intrinsic to the fact that you are just using a frame to measure a property and the event must be the same regardless of frames.
That's a simple contradiction, not a paradox. I'm deliberately contradicting the assumption that everything has to be the same across all frame, to see what the contradiction buys me, and what's left of what we'd normally expect.
Toss away relativity and you still have the problems with thermo etc etc. There is something intrinsic to the fact that nothing can go back in time.
First of all, I'm not tossing relativity completely away... I'm keeping time dilation, the light-speed limit for all information-bearing interactions other than the special FTL messages, a Minkowskian spacetime geometry, etc.
I'm mostly keeping the idea that nothing can go backward in time. Nothing can go backward in time in the preferred frame, and in other frames, all backwardness is non-local.
Here's a painfully forced analogy for what I'm trying to do... Consider three proposals for changing the rules of baseball.
1) Replace the baseballs with oranges.
2) You aren't allowed to hit the ball.
3) Pitchers must bat for all team members, and only those team member, who don't bat for themselves.
Given Proposal 1, you could just dig in your heels and say "Well, if you don't use baseballs, it isn't baseball anymore, is it?" and stop there.
Or you could explore the idea, "Well, it would certainly be a messier game. I don't know if the outfielders would have much to do anymore, since it'd be hard to hit an orange very far. Say, can we freeze the oranges? Etc., etc." The game would be quite a bit different, but something still recognizably baseball would survive. Things wouldn't be so broken that you couldn't discuss consequences.
Given Proposal 2, with no options given for something else you're allowed to do instead of hit the ball, it's pretty clear that you?d outright kill the game off with the rule change. All players could do is stand there until they strike out, and no one would ever score.
Proposal 3 doesn't merely break the game, it leads to a logical paradox in which you can't define whether or not the pitcher must or must not bat for himself.
For my FTL proposal, I want to see if it can at least hold up on a Proposal 1 kind of level.