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[kaijyuu]

Re: Going faster than the speed of light and time travel.


Here's the conundrum. First you have to realize that the faster you go, the more space constricts and the slower time moves for you (relative to others). Going to Alpha Centauri at .9999 the speed of light will not take 4 years for you... far less, in fact. That's because, from your perspective, space shrunk and you don't have to travel nearly that much distance.

At the speed of light, space constricts to infinitely thin; you reach your destination, no matter how far away, instantaneously. To outside observers yes, you're going to take as much time as light takes. But not to your perspective! To you, it was a mere instant. To you, the distance between origin and destination was 0. Good luck hitting the brakes in time.

So what happens going faster? Does space get less than infinitely thin? Can you reach somewhere faster than instantaneously? The only way to go is back in time. You get there before you left... at least from your perspective.

[Loud Whispers]

Re: Going faster than the speed of light and time travel.


Here's the conundrum. First you have to realize that the faster you go, the more space constricts and the slower time moves for you (relative to others). Going to Alpha Centauri at .9999 the speed of light will not take 4 years for you... far less, in fact. That's because, from your perspective, space shrunk and you don't have to travel nearly that much distance.

At the speed of light, space constricts to infinitely thin; you reach your destination, no matter how far away, instantaneously. To outside observers yes, you're going to take as much time as light takes. But not to your perspective! To you, it was a mere instant. To you, the distance between origin and destination was 0. Good luck hitting the brakes in time.

So what happens going faster? Does space get less than infinitely thin? Can you reach somewhere faster than instantaneously? The only way to go is back in time. You get there before you left... at least from your perspective.

TIME IS RELATIVE NEUTRINOS

[Starver]

Multiple quotes from multiple posts, easier to edit off-board, but lost all the references.  Sorry.  But this way, I splurge one larger message rather than splat several still-not-small ones.

Imagine you fly away from Earth at relativistic speed. To you, time is passing slower for Earth than for you. After a day, you use your neutrino ftl communications to tell them you forgot to turn the oven off. Since (from your reference frame) time is passing slower for Earth, they receive it in 12 hours. They turn the oven off, then send back a message that they have done so. However, from their frame of reference time is moving slower for you than it is for them, so you receive the reply 6 hours after you left; 18 hours before you send the original message.

I still don't see that.  The key point is that when you're talking about FTL communications between us and Alpha Centauri, you're talking about two worlds (roughly) in the same reference frame, just separated.  You do not expect to see the visible beacon saying "I have received your FTL message" in the 4yo images.  You would expect to see that in four years' time, regardless of when you received the FTL reply.  When you're making FTL communications between vastly differing frames (Earth and the ship going, for the sake of the half-speed time dilation, at 0.75c relative to it... or the other way round) your relative communication times would seem to be only comparable to a common point of correlation.

Let's say that, perhaps, the FTL message sent (ship time) after 24 hours will arrive on Earth after 24 hours (earth time) has passed.  Just imagine you had taken one end of a wormhole with you[1].  Stepping through after 24 hours takes you to 24 hours (+ transit time) after departure on Earth, and stepping back will take you to 24 hours (and double transit time) after departure for the ship.

Thus this 'instacomm' signal will also arrive on Earth 24 hours (local time) after departure, and the instacomm reply 24 hours-and-a-bit (ship time) back on the ship.  This is for the instantaneous connection, which might be a special case.

If it's 'merely' a 1.5c speed signal then time (increasing time) will pass in each direction, as it has to 'catch up' with the other retreating party.  Not as much time as in SoL communication, but still increasing time.  And still less "arrive before it is sent" possibility, although "arrive before the SoL beacon indicates" is expected.

e.g., by Earth time, the "24 hours on ship" occurs at 48 hours into the mission, with the ship at .75c having gone 1.5 lightdays away.  The 1.5c signal will then take 24 (Earth) hours to get back, arriving as three days of mission have passed.  The 1.5c signal then has to travel the 1.5 lightdays plus another three days of travel (1.5c signal goes 4.5 lightdays from Earth, in that time, ship went from 2.25 lightdays away, to the point 2.25 lightdays further away before being caught by the reply).  144 hours total reply-time, it can be reasonably assumed at the Earth-end.

Obviously under ship-time it's another measure, but by the same calculations the original signal 'catches up with' Earth one day later (end of day 2, ship-time, when Earth is an apparent 1.5ld away) and the response arrives a further day later.  So perceived response time on the ship is after 72 hours.  Not before it was sent.  And if the ship tells Earth this, they get confirmation that time is being experienced on the ship at half the rate, as observed.  (Now look at sending a signal from Earth and getting a reply, and making the same calculations.  The ship also sees the Earth as experiencing half the time between initial sending and receipt receiving, confirming to them that the Earth has slower time.  Dialogues between ship and Earth will continually exhibit such doubly-asymetrical perceptions of time, the relative differences of perception staying the same but the increasing distance meaning longer and longer waits being accepted in such calculations.

(The above done in my head, you'll doubtless find at least a typo or two, if not an outright thinko.)


So, anyway, regardless of instanaity or not, while you and they are travelling away from each other, the other's respective times are looking slower to each observer through standard SoL methods, but you know that you are seeing the other party's delayed light.  Just like in sending between Sol and Alpha Centauri, you know that the FTL signal has been received and replied to, but you are still seeing the 4yo image of the other party.

[...]once you have a signal sent back in time to the original point, there's nothing stopping you looping it through again, and sending it back still further

As per the 'jiggled wormhole' idea, and other similar time-travel constructs: if possible there would be a limit, that of the creation of the unit (or, indeed, mission) which is capable of sending/receiving such messages.

The bullet strikes and kills a victim who's death is the event marked "*" in Diagram 8-1 . This event occurs after the passing event in Op's frame of reference, but it occurs before the passing event in O's frame.

As I understand it, it is only observed at different times.  Necessarily there has been SoL delays to one or other party's observations.  But that is perhaps where I fall down on the understanding of this example.  There is no 'universal' now, or single time-frame from which to judge all others, but a lot of the theory seems to be that "when you receive the signal it is the same 'now' as was sent".  Which is equally nonsensical.  There has obviously been a delay.  (The photons used to communicate might argue, they got there straight away, and (if directly reflected) got back straight away, and yet time had passed at the destination.  Twins' Paradox in extremis, for a traveller for whom the rest of the universe is moving around at light-speed relative to it, except that from a photon's POV the rest of the Universe's dimensions (time and space) effectively do not exist.)

I haven't been able to do much more reading of that, though.  I spent last night drawing various time-cone diagrams in my head to try to address the 'break-out signals' issue, and came up with the conclusion that there was no case, but I've been a little hard-pressed here at work, this morning (is now well into 'this afternoon') so may still be missing the point.  I have previously been exposed to this apparent paradox, and so might be biased to the opinion that I gathered at the time, so I really did want to spend more time on this particular explanation.

So what happens going faster? Does space get less than infinitely thin? Can you reach somewhere faster than instantaneously? The only way to go is back in time. You get there before you left... at least from your perspective.

The equations used indicate the numbers become imaginary (square root of minus one, or various multiples/fractions thereof).  Imaginary numbers are interesting but not 'real' and thus not easily worked into expectations.  Then again, when I first told my fellow primary-school friends about "negative numbers", I was pointedly disbelieved.  Not sure I understood it at the time, actually, but it made good sense.  (Easily imagined as if you're on a staircase on the ground floor (1st floor, for any of you 'merkins) and go up three floors and down five floors, you're now in the second basement level.)  But while negative numbers are often used in real life (e.g. your debts!), imaginary ones are still the largely preserve of either the pure mathematician (e.g multi-root calculations, and in visualising some types of fractal) and to help answer some questions in physics (e.g. electromagnetic waves) before the point at which 'reality' returns.  Having it stay imaginary is still beyond most practical imaginings.  And probably would be impossible to 'experience' first-hand anyway.





[1] We get, here, into the old "jiggle one end of a wormhole around relativistically[2], before returning to the source.  Then we may get time-travel effects, because the ends now have (near)-instantaneous SoL communication.  This is more complicated, however, than a straight departure from Earth at 0.75 c, as it involves not just one distinct frame of reference (after the initial acceleration has been accomplished), but a changing one.  To which further complications seem to apply.  I suspect that some aspect of the variously accelerating frames of reference (as opposed to the normal trivialising away of the boost and deceleration phases) comes into play given the need to decelerate and reverse the journey.  Technically it applies to the accelerative phase of the 'simple' example, of course.  And, I note, the concept of acceleration in the Twins' Paradox is noted in other posts that I'm now reading but not involving myself in right now.

[2] e.g., send the wormhole to AC and back, at 0.75, taking 4 years total ship-time, but eight years Earth time, arriving at AC.

[palsch]

There is a really nice discussion of this whole question here, with diagrams and why it doesn't necessarily apply to this case. I'm going to have to quote quite liberally here.

The problem is the following: Alice is a really hot girl and has a crush on Bob, but of course only as long as Bob does not call her first. If Bob calls first, he will appear too eager for a date and totally lame in Alice’s mind. Now it is already 12 o’clock on Saturday and Bob is a popular hunk, so Alice better waits no longer; she sends an infinitely fast tachyon to Bob, meaning relative to Alice, the tachyon starts (event P) and arrives (event Q) both at twelve o’clock, that is t = 12h.

Spoiler: "Diagram" (click to show/hide)

...
Now where is the problem? The problem starts if on reception of the tachyon, Bob is allowed to perform the same procedure that Alice did, namely, he may immediately hit the answer button by accident and send the tachyon right back to Alice in the same manner as Alice did: The tachyon is starting (event Q) at t* = 12h and arriving (event R) instantaneously at the same time t*= 12h, too, but this time relative to Bob’s time t* because he is sending it. The situation is symmetric to that described before; Alice moves away from Bob because Bob moves away from Alice. No different from before, such implies that according to the receiver’s time coordinates, the sending happened one hour later. If the sending (event Q at t = 12h) happened one hour later, it must be now one hour earlier when receiving it (event R at t = 11h).

Spoiler: "Diagram 2" (click to show/hide)

Picture stolen and then marginally altered - hope nobody sues me for this.

Alice started the whole business at t = 12h but she receives the answer from Bob before that at t = 11h. This cannot possibly be, because Alice is very attractive and would not send any message to Bob at all if he contacted her first and moreover at 11 o’clock on a hung over Saturday morning. Causality is violated.

Note that the diagrams are stolen from here, which has a slightly more in depth and formal discussion, but I prefer this phrasing.

But essentially this is dealing with the relativity of simultaneous events. Unless both Alice and Bob are in exactly the same reference frame they will disagree about what events are simultaneous, and so an instantaneous transmission for one of them won't be for the other.

The whole second part of that post is about why this may not apply, especially in cases where there is a favoured reference frame (his example; the CMB) which such signals travel relative to.

Relativity works because of the symmetry of reference frames; absolutely none is favoured over the other and all are equally valid. If I observe event A occur before even B and you observe event B before even A we are both right; there is no absolute order for events outside of such reference frames. Introducing a limiting frame on FTL travel removes that symmetry and so restricts causality breaking.

I'm trying to summarise the simpler example argued over in the comments on that post. Imagine you can encode an instantaneous transmission in the CMB reference frame (eg, the signal is instantly spread throughout the entire CMB in it's rest frame). Alice can now send the same transmission to Bob from t=12 to his t=12. But now when Bob sends his reply it travels instantaneously in the frame of the CMB. That is, Alice's frame. Instantaneous transmissions are only possible relative to that one frame and so an instant reply from Bob at t=12 would reach Alice at t=12 as well rather than t=11 as we found before. Anyone moving relative to the CMB would see the signals travelling through it at different, non-instant speeds.

Of course there is no reason to assume the CMB is such a preferred frame, but it is possible to imagine a system where faster than light travel depends on a given reference frame in most situations, and so causality violations are - if not entirely impossible - at least very, very hard. You only get causality breaking when you have two different reference frames allowed FTL signalling.

[Starver]

I see no problem with Alice and Bob in Diagram 1 (well, apart from any other problem regarding their relationship).  It being a tachyonic message transfer, Bob's receipt at 12:00 is perfectly indicative of it being sent at 12:00, and Alice's receipt of the reply at 12:00(:30-ish) indicate it being sent at 12:00(:30-ish).  If Alice had received a SoL signal from Bob's frame at 12:00, then it would have obviously been sent at 11:00.  But at 11:00 in Bob's time-frame Bob was still an hour away from receiving Alice's signal.

If Bob's timeline frame of reference was delayed (Twin Paradox-like?) in a way not tied to the instamatic communication method then he might have received it at 11:00, but the reply would still arrive back at 12:00:30, or so.  Bob, impetuous replier as he is, probably would not mind that Alice looked a bit more eager.

Problems would arise if (for various reasons) the tachyonic transfer was actually sent back in time, as tachyons are reputed to do, with an angle of message transfer between the respective lightcones not being strictly 90 degrees to the major axis, but actually backwards in direction, and thus the reply by similar means goes back twice as much.


But, as I said before (in passing) I've got this 'romantic' idea that time-travel complications are inbuilt into the universe.  Its utterly irrelevant to the above example but, if temporal loops are possible, I could see Alice's message arriving at Bob shortly after they (somehow, diverging timelines allowing) had separated just after the date, Bob didn't mind (or notice) the apparent impetuousness and sent "I'd like to see you, soon!" to a pre-date Alice and thus inadvertently propositioned her for the date that had (at the start of this example) just occurred!  (What then happens, when Alice doesn't get an apparent response to her post-date communique is left up to the Universe...)


Diagram 2 just seems wrong, to me.  Either the Q->R line should impact Alice's timeline above/after P (rather than below/before it) because the perpendicular tachyonic signal points upwards from the offset B-line, or the simultaneity of P->Q should count the same for Q->R, i.e. R==P.  (Whether or not Q and P are at the same latitude in the diagram, but I'd say that they have clearly separated in the amount of time-passed and thus the preset communication system would arrive higher up the B-line and then bounce back to R==P on the A-line, albeit plus the thinking-time delay.)

In the case of converging timelines of Alice and Bob I could see an R on line A being in the 'past' to P, if communication is perpendicularly away from the B-line and struck the A-line in the past.  I think this is the best argument against there being an arrangable insta-communication between two heretofore separate timelines.  i.e. that they need something (entangled pairs of particles/whatever) set up somewhere.    I acknowledge that it still causes problems if a mechanism is set up between once identical timelines in which one departs and then starts to 'return' again, because then there's the possibility of one line (the B) taking SoL information from the A-line's lightcone 'wake' that it can send to the A-line along its quantumly-connected communication system actually to a point well before the event.

This is the point where I see the possibility that causality breaks, and where (in the grand scheme of things) I envision that the stability of the universe relies upon such things as self-fulfilling prophecies in order that it has ever existed in that state.  (I'm not talking about someone/something finding the problem and wiping it out, but that the tapestry of the universe that contains such contradictory loops of thread does just not form an existence, in the metaverse within which universes of all kinds are floating.)  But that's well beyond the original remit and I'll admit that my preference for universal self-consistency (not a factor in the general P->Q->R analysis) is something that colours my appreciation of various time-travel fictions.  But I don't deny "new branch" paradox resolution, travel only to parallel (disjointed, but representing similar histories) dimensions and other solutions to that.

Indeed, apparent time-breaking communications could be messages from partnered universes, in a stack.  Until the discrepancies build up it might appear to be genuinely same-universe.  Maybe (wow, somehow back on track to the OP, here) those discrepancies include our OPERA sensor receiving neutrinos that came from another universe's CERN-generated neutrinos, only with a small temporal difference.  (Either because other-universe is slightly disjointed, or because things meant the other-CERN scientists managed to eat their lunches just a little bit quicker.)  And, in case you're wondering, their OPERA sensors received CERN>>2's signals, and that's why they're repeated their sending (to us), all the while receiving the neutrinos originally intended for OPERA>>2's sensors due the latter receiving CERN>>3's neutrinos earlier than CERN>>2's ones should have hit.  And meanwhile, our neutrinos are pestering OPERA<<1's sensors so that CERN<<1 needs to send more experimental neutrinos, inadvertently giving OPERA<<2 the impression a continuing supply of (what they think are) CERN<<2's neutrinos are misbehaving.

No, that isn't my theory as to how this whole thing arose, merely a logical extension of the time-transit==universe-shift idea.

[Bremen]

Multiple quotes from multiple posts, easier to edit off-board, but lost all the references.  Sorry.  But this way, I splurge one larger message rather than splat several still-not-small ones.

Imagine you fly away from Earth at relativistic speed. To you, time is passing slower for Earth than for you. After a day, you use your neutrino ftl communications to tell them you forgot to turn the oven off. Since (from your reference frame) time is passing slower for Earth, they receive it in 12 hours. They turn the oven off, then send back a message that they have done so. However, from their frame of reference time is moving slower for you than it is for them, so you receive the reply 6 hours after you left; 18 hours before you send the original message.

I still don't see that.  The key point is that when you're talking about FTL communications between us and Alpha Centauri, you're talking about two worlds (roughly) in the same reference frame, just separated.  You do not expect to see the visible beacon saying "I have received your FTL message" in the 4yo images.  You would expect to see that in four years' time, regardless of when you received the FTL reply.  When you're making FTL communications between vastly differing frames (Earth and the ship going, for the sake of the half-speed time dilation, at 0.75c relative to it... or the other way round) your relative communication times would seem to be only comparable to a common point of correlation.

Let's say that, perhaps, the FTL message sent (ship time) after 24 hours will arrive on Earth after 24 hours (earth time) has passed.  Just imagine you had taken one end of a wormhole with you[1].  Stepping through after 24 hours takes you to 24 hours (+ transit time) after departure on Earth, and stepping back will take you to 24 hours (and double transit time) after departure for the ship.

Thus this 'instacomm' signal will also arrive on Earth 24 hours (local time) after departure, and the instacomm reply 24 hours-and-a-bit (ship time) back on the ship.  This is for the instantaneous connection, which might be a special case.

If it's 'merely' a 1.5c speed signal then time (increasing time) will pass in each direction, as it has to 'catch up' with the other retreating party.  Not as much time as in SoL communication, but still increasing time.  And still less "arrive before it is sent" possibility, although "arrive before the SoL beacon indicates" is expected.

e.g., by Earth time, the "24 hours on ship" occurs at 48 hours into the mission, with the ship at .75c having gone 1.5 lightdays away.  The 1.5c signal will then take 24 (Earth) hours to get back, arriving as three days of mission have passed.  The 1.5c signal then has to travel the 1.5 lightdays plus another three days of travel (1.5c signal goes 4.5 lightdays from Earth, in that time, ship went from 2.25 lightdays away, to the point 2.25 lightdays further away before being caught by the reply).  144 hours total reply-time, it can be reasonably assumed at the Earth-end.

Obviously under ship-time it's another measure, but by the same calculations the original signal 'catches up with' Earth one day later (end of day 2, ship-time, when Earth is an apparent 1.5ld away) and the response arrives a further day later.  So perceived response time on the ship is after 72 hours.  Not before it was sent.  And if the ship tells Earth this, they get confirmation that time is being experienced on the ship at half the rate, as observed.  (Now look at sending a signal from Earth and getting a reply, and making the same calculations.  The ship also sees the Earth as experiencing half the time between initial sending and receipt receiving, confirming to them that the Earth has slower time.  Dialogues between ship and Earth will continually exhibit such doubly-asymetrical perceptions of time, the relative differences of perception staying the same but the increasing distance meaning longer and longer waits being accepted in such calculations.

(The above done in my head, you'll doubtless find at least a typo or two, if not an outright thinko.)


So, anyway, regardless of instanaity or not, while you and they are travelling away from each other, the other's respective times are looking slower to each observer through standard SoL methods, but you know that you are seeing the other party's delayed light.  Just like in sending between Sol and Alpha Centauri, you know that the FTL signal has been received and replied to, but you are still seeing the 4yo image of the other party.

[...]once you have a signal sent back in time to the original point, there's nothing stopping you looping it through again, and sending it back still further

As per the 'jiggled wormhole' idea, and other similar time-travel constructs: if possible there would be a limit, that of the creation of the unit (or, indeed, mission) which is capable of sending/receiving such messages.

The bullet strikes and kills a victim who's death is the event marked "*" in Diagram 8-1 . This event occurs after the passing event in Op's frame of reference, but it occurs before the passing event in O's frame.

As I understand it, it is only observed at different times.  Necessarily there has been SoL delays to one or other party's observations.  But that is perhaps where I fall down on the understanding of this example.  There is no 'universal' now, or single time-frame from which to judge all others, but a lot of the theory seems to be that "when you receive the signal it is the same 'now' as was sent".  Which is equally nonsensical.  There has obviously been a delay.  (The photons used to communicate might argue, they got there straight away, and (if directly reflected) got back straight away, and yet time had passed at the destination.  Twins' Paradox in extremis, for a traveller for whom the rest of the universe is moving around at light-speed relative to it, except that from a photon's POV the rest of the Universe's dimensions (time and space) effectively do not exist.)

I haven't been able to do much more reading of that, though.  I spent last night drawing various time-cone diagrams in my head to try to address the 'break-out signals' issue, and came up with the conclusion that there was no case, but I've been a little hard-pressed here at work, this morning (is now well into 'this afternoon') so may still be missing the point.  I have previously been exposed to this apparent paradox, and so might be biased to the opinion that I gathered at the time, so I really did want to spend more time on this particular explanation.

For the first part with Alpha Centauri, you're correct; if no party is moving relative to another slower than light, then FTL cannot be be used to violate causality.

For the second, and this is what gave me trouble too, you're assuming that there is some universal standard of time; IE, that at any one moment every reference frame is existing at a certain state, with only the rate of change being different. But according to special relativity this isn't true, that time is relative just like motion (because it *is* motion, in a way). You also seem to be thinking that you observe clocks in other reference frames ticking slower because their light is taking longer to reach you; consider that you also see their clocks ticking slower if they are approaching you.

It probably looks like this is completely illogical. This is because it is if you allow for any ftl or universal means of syncing clocks; with the universe limited to lightspeed communications, everything ends up working out as you can never quite catch that what's happening is incredibly bizarre and verging on impossible. This is why the idea of ftl neutrinos makes physicists wake up in cold sweats.

[MonkeyHead]

I wake up in cold sweats most nights simply because I am a Physicist. I just hope an anthropic principle argument works well here. As reality and causality isnt fucked up, it would appear FLT travel, Time travel, or either of the 2 involving information transfer simply isnt possible.

[GlyphGryph]

Eh, not really. Assume for a minute causality is, in fact, fucked up.

How would you know?

I mean there are plenty of possible ways it could get fucked up, in my mind, that would leave us none the wiser. Once you've broken the concept of causality, time becomes less like a stream and more like a movie - you should be able to cut out, replace, or alter large swathes of the film without effecting the rest, right?

[MonkeyHead]

Ok, a more accurate statement is that the arrows of time still seem to point in the right direction based on life experince...

I dont remember tomorrow. My CPU doesnt have files on it form the future. Without actually going to measure the red shif of a galaxy, the universe is still expanding. The plate I just dropped fell downwards and didnt reassemble. My laptop is dissipating heat the universe in the way entropy suggests it should. I assume I would notice diferences in these behaviours compared to what I would normally experience.

We would notice at least one of the arrows of time to not allign with the others right?

[Osmosis Jones]

Sometimes I get messages on my phone time stamped from 2 or 3 minutes ahead... sheeet, I have a timephone :O

As to the whole wall o' text relativity discussion I missed, there isn't really much to add, as Bremen did as good a job explaining it as I ever could. All I can do is really stress the requirement that the observers be moving in different reference frames (The example I used that finally swung it for me was using a third reference frame as an intermediary; Say Alice to Bob to Charles and back again, with Bob stationary and the other two hairing off in random directions. Dunno why, just seemed to make more sense in that one), and that there is no universal reference frame. If only there was, relativity would have been a far simpler subject

But while negative numbers are often used in real life (e.g. your debts!), imaginary ones are still the largely preserve of either the pure mathematician (e.g multi-root calculations, and in visualising some types of fractal) and to help answer some questions in physics (e.g. electromagnetic waves) before the point at which 'reality' returns.  Having it stay imaginary is still beyond most practical imaginings.  And probably would be impossible to 'experience' first-hand anyway.

Imaginary numbers have a lot of uses, in virtually anything that has a periodic component; fully aside from EM waves, there's AC circuits, structural vibrations, solid-state physics, chemical surface layers (using Nyquist plots) and much, much more. To be honest, the people I know that use them the most are engineers, and you can't argue that engineers are mainly theoretical

I can guarentee that there is something within one metre of you that would not exist if not for someone's understanding of imaginary numbers.

[kaijyuu]

So what happens going faster? Does space get less than infinitely thin? Can you reach somewhere faster than instantaneously? The only way to go is back in time. You get there before you left... at least from your perspective.

The equations used indicate the numbers become imaginary (square root of minus one, or various multiples/fractions thereof).

That actually makes sense. Righto, consider my time machine even more improbable.

[palsch]

OK Starver, I think there are two points here.

Firstly, you seem to keep coming back to delays due to the speed of light. In relativistic physics we assume these are always taken into account. That is, all parties are aware of the speed of light. Anyone working out the order of events will include signal delays in their calculation. This is a basic assumption of such problems.

The other...

Diagram 2 just seems wrong, to me.

Diagram 2 is right. The link I gave after the quote makes it more explicit about how these Lorentz transforms work.

Spoiler: "Diagram 3" (click to show/hide)

Here you have two reference frames overlaid. We are in the white reference frame. The blue frame is moving left to right at 0.4c relative to us. The blue lines show lines of simultaneous events in space (the space line - two events are simultaneous if they fall on the same space line) and similar locations in space (the time line - eg, the path followed by an object sitting in one spot would be along the time line). It's trivial to see from this how the two frames disagree on the order of events P and Q. Given the two frames are fully symmetric (eg, neither is favoured) there is no actual order to the two events. You can't say P actually happens before Q or vice versa without clarifying which frame you are talking about.

A simultaneous signal passing between two people travelling in a reference frame moving at 0.4c relative to us would look like this;

Spoiler: "Diagram 4" (click to show/hide)

Which brings us back to Diagram 2.

Technically we would need to break out the relevant maths to prove all this, but these diagrams are right and accurately illustrative of how instantaneous signals would look in a relativistic universe. I'm just going to go ahead and type out a complete example using an intermediate observer to see if that helps. Hidden for length and probably repetitiveness.

Spoiler (click to show/hide)

Let's say that two events, (A & B) occur at time t = 0 in your reference frame. To work out the time of that event in my reference frame we use the equation;

Here v is the relative velocity of the observers (we will both agree on this) and x is the spacial location of the event along the axis of movement in your reference frame. t is your observed time, t' is mine.

In the case where my velocity is positive along the x-axis (and the only movement in these cases is along the x-axis; that's the definition of the x-axis), but where the two events happen at different points, it's trivial to see that they will have different times from my point of view. One will occur before the other. Let's say A happens first, then B.

Now introduce a third party moving in the opposite direction. They will also observe the two events happening one after the other. However, because their movement has the opposite sign to mine the order they occur in will be reversed. B then A.

If we had a signal instantly transmitted from A to B.

From your point of view it would be instantaneous communication.
From my point of view it would be FLT, but take some time.
From the other point of view it would arrive before it left.

We can generalise this now to any faster than light velocity, given the right reference frame. Go back to Diagram 3 above and notice that the light cones are the same for both, but the line of simultaneous events (labelled space) is angled in the blue frame (which is travelling left to right).

In the white reference frame, Q occurs before P. There is a temporal separation though, so we don't need an instant signal between them, just an FTL one. However, because in the blue frame P occurs before Q we will still see a signal being sent back in time, even though it wasn't instant in either frame.

None of this really ties into the CERN results that well, it's just interesting to look at how FTL works with the universe we know.

[Starver]

Long combined reply was typed, but it is horribly long-winded.  So Ctrl-A, Ctrl-X, and start again.


Bremen: I'm not assuming a universal standard, I was dealing with subjective impressions of time.  The only standard I've assumed in the examples is that a given space-time location in each Frame was once coindicent (and, as far as I can tell every frame has such points, here they're Earth and the now retreating Space-Ship who share such a heritage point at Earth at the time of launch) and thus a usable datum point.  A different location in the same frame has different impressions.  If we accept an observer on Pluto is in Earth's frame, for all intents and purposes, the ship passing (or, conversely, travel even more distantly away) can still be observed to have slower time but there's different response-times and differently accounted-for adjustments for the time-delay of information (SoL or FTL).  Ditto in reverse.)

And Doppleresque effects (you didn't name it, but I think you think I was describing it) is something different, and not a part of the equation.  Compare this with an object retreating (or being retreated) from another, reflecting a signal off of it and getting a doubly-Dopplered signal back to measure.  Under non-relativistic circumstances the "bounced-from" party can work out what frequency the other should be able to measure.  In the example, one party measures the return-time and the other party calculates what they think it should be, and yet they find (when communications about that particular cycle can be finalised) that they disagree.

I didn't think I'd even referred to a ship approaching the Earth at relativistic speeds (it was always an outbound mission, in my head) but I did make similar calculations for such a second example (that I decided not to post) and perception of time (by each party, regarding their counterpart) was identically asymmetrical.  Yes, two-way communications would be more frequently replied to, but the apparent time that any particular 'bounce' took was still reported as slower than the 'stationary' party (i.e. alternate observer) would nominally have believed to be the case.


Osmosis (loved your film, BTW...), I perhaps gave imaginary (and complex) numbers short-shrift.  But I wasn't saying that they didn't have a use, but just that people (regular people; I definitely should have added electrical engineers to the physicists and maths bods I mentioned, though, even though they generally use a different letter for it ) don't get to use them in everyday life, and a lot who do 'use' them have them being calculated (or pre-calculated) on their behalf without needing to concern themselves with the specifics.  Consider myself chastised at this and any further omissions, in this field, however.


Palsch, the delays I was indicating I was indicating as already assumed.  Given instantaneous responses in the example (that I think you're referring to), it was measurements of the delays inherent in the SoL (or, as it was, 1.5c) communications, but the disagreement was between the perceptions of said delays.  Some might say "double-blinded" by the fact that it was a sum total of two separate legs of the journey (to each observer, one leg in which the distance was from a definite point of the retreating opposite number, and one leg in which they themselves were sending a signal to 'catch up' with the other... but in a different order), the sum total of which is then compared and found... different.  If I have confused matters (or "have matters confused"), apologies.

However, on to something that is rather more of an apology: Your newly extended quote has explained one thing to me.  Whether by misreading or not reading or (as you surmised, correctly) me not actually going to the full link, I did not fully comprehend the 'space' axes for what they were.  Last night I'd realised that the strange blue diagonal line (along which Q->R travelled) existed, behind the given red line in Diagram 2.  I realised this only as I was GIMPing those first two images to demonstrate my own thoughts.  Prior to this, I had thought that the white horizontal was the "equivalent now" line, then I switched to the viewpoint that actually the blue line more agreed with an "It is <x> O'Clock" shared impression.  As such, I had a rearranged version of Diagram 2 which looks (with such displaced time-cones) very much like Diagram 4, except with a 'ladder' of times[1], only with one on the left being "event P+R" and its linked to one on the right being "event Q".  (Won't bother posting these various images, their original purpose has been rather overtaken by more recent understandings.)

Anyway, this was by way of being a "I have one end of a communication system, you have the other" bidirectional link, in diagram form, where communications occurred so that t_Alice==t_Bob.

I do see now that an independent and unidirectional sending of a signal by Alice to "Alice's now, but elsewhere" (same time, different place, in the white timeframe), that is aimed at Bob, and a signal by Bob to "Bob's now, but elsewhere" (ditto, but on the blue), aimed at Alice, gives this disjoint.  In the original snippet about the issue I never did derive that particular aspect.  But I've always been imagining instant communication as being by an artefact system (entangled particles/whatever).

Makes me wonder if you could get an entangled transceiver to the point in space-time that Q represents (and which is connected to one that stays on Alice's time-line, i.e. through both P and R) without the full relativistic effects that Bob has experienced.  If not[1], then I think I could state that the T(Alice)@R == T(Bob)@P, but I have doubts.  A secondary consideration, of course, is that this is just diverging frames[3].

It still leads to complications when Bob adjusts his velocity so that his absolute position (not including time) in his adopted frame of reference is now converging again with Alice's absolute position (ditto) in hers.  Because such a communications device that Alice has already given to Bob before his original travelling is now capable of sending to the "same here, different now".

Actually, it's Bob that can cause the real problems (assuming it's not Alice using it as a spy-glass), because he has the "less aged" one (in the simpler example of the Twins' Paradox domain) and thus when he arrives back at Alice he can communicate with Alice at the point before his arrival.

(But, regardless, he cannot communicate to Alice prior to his original departure, and there will be significant time throughout Bob's journey that his information to Alice cannot possibly include any knowledge that Alice does not already know.  He has to re-enter Alice's device's light-cone (originating on the timeline point at which her artefact has the same age as his does "in the future") before there's a potential for temporal loops that need to be explained away as either "feedback until steady", fully flip-flop the universe(s) or plain "can only exist at all if they don't cause issues".  But that's back to the philosophy of temporal mechanics, in lieu of some actual practical experience with such potential paradoxen. )


Being again limited by time (none of the day just passed has been able to be used to read, so I am freshly reassessing this latest correction, and I've only just rushed through this thread) I'm not anywhere near a position to respond to all the other good points.  Including the Relevant Maths spoiler, which looks Ok at first sight, certainly.

(And, yes, the first attempt at response was far longer than this.  I am notably useless at making an understandable summary, and imagine that this cut version is no exception to this rule.)



[1] Not relevant, but based upon the dimensions and given times for the events, I worked out that Bob and Alice's times and places would have agreed at between 4AM and 5AM that morning.  So they could have still been together well past midnight.

[2] And right now my mental arithmetic isn't clicking into place enough to work out the total dilation of, say, a journey to Q from a space-time point twice as far back along line A as the A/B origin is from R.  Half the speed, but takes longer.  Normally I'd say it was equivalent, but it's by no means linear.

[3] A tertiary thought is regarding a device-pair set up significantly early in Alice's history so that while one half retained until Bob departs, the other half is sent in advance to be retrieved by Bob at space-time location Q.  This shares very many similarities with the situation of Bob returning his half of a particular pairing to a point where Alice can directly compare it with her retained example.  And one further reason for me to doubt that "it all works out the same in the end", regardless of which frame(s) of reference the items take (and here I'm talking of magnitudes of velocity that are relativistically distinct, yet still sub-lightspeed) to get from one point in spacetime to another.   In fact, if we fully take Bob's away-from-Alice frame and his towards-Alice frame as distinct aspects, this actually closely relates to the original description of "three different observers having three frames" giving the opportunity for temporal anomolies.  So... I suppose I have managed to persuade myself that the originally doubted phenomena exists after all.  QED?

[Osmosis Jones]

So... I suppose I have managed to persuade myself that the originally doubted phenomena exists after all.

Welcome to SCIENCE!

[MonkeyHead]

On an unrelated note, I still havent messaged myself from the future yet. Poor show, future me.