I like to imagine that as soon as we discover FTL and break spacetime, the simulation crashes and the higher beings are annoyed they have another bug to fix

"The universe is not required to be in perfect harmony with human ambition." -Carl Sagan

If FTL does exist, the universe might have some way of blocking any information/matter from interacting with the ship/crew travelling FTL. Similar to how the event horizon of a black hole stops any information from escaping it where time and space flip beyond it ( which would also break causality if information could escape ).

It's very rare and special when someone can explain such a complicated topic in an easy to understand and follow way. Thank you.

Does anyone realize how crazy it is that we can even theorize something like this

There once was a young lad named Mike. Who could run faster than the speed of light. He took off one day, In a relative way, And returned on the previous night!

I watched the entire video, and I get the sense you broke the rules of your own diagram. You drew two diagonal lines at the start, indicating the speed of light. You set the premise that any line between the time axis and this diagonal line is something moving slower than light (STL). Any line between the diagonal line and the space axis are faster than light (FTL). You then start speculating about FTL transmitters able to send a message instantaneously, meaning horizontally to the right. I'm with you so far. This is where you break every rule that has been set. You draw a line that goes downward. We've not established any reason why a line would do that. Your made up transmitter can only go up to a limit of a horizontal line (instantaneous messaging). These paradoxes start popping up because you've suddenly decided this message is being sent to the past. The FTL transmitter is now a time machine for no reason. Like I said there might be some physics I don't understand. However in the diagram you've been using, there has been zero explanation of why any line would ever go down. The established rules were that lines could only be in the STL or FTL directions. Once you start going downward you break your own rule set.

What if the solution is a combination of two rules? 1. Anything that is going FTL cannot physically interact with anything going STL. 2. When exiting FTL, your world line is also precisely what it was before you engaged FTL. For example, an FTL ship cannot instantly travel to an STL ship, and exit out of FTL with zero relative velocity to the STL ship. This would make the STL ship intercepting an FTL message impossible. The only way to send messages FTL is by way of literally sending a physical ship that exits out of FTL at the destination. A message that simply travels through space and can be arbitrarily intercepted by any observer is just not possible. The FTL ship could also fly out to the STL ship at FTL, but in order for it to ever get back to Earth earlier than it left, it would have to accelerate to have a zero relative velocity to the STL ship from this example. But then that acceleration would take time, preventing it from getting to Earth before it left. I dunno, I’m no physicist, so I feel like I have to be missing something here, because that type of restriction doesn’t feel too arbitrary to me. This could just be me not yet picturing some other diagram following those two rules that still break causality. Seems like the isolation within FTL, and your relative velocity from your departure being conserved in the jump, both feel like they might be more of like natural consequences of how an FTL drive might actually work.

Well, I don't know about time travel, but a fascinating thing to think about is that if you could travel FTL and have a way to look at earth from any distance, you could go far enough away from earth to see the past.

"It almost seems like a cruel cosmic joke that the universe be arranged such a way that we are able to look out and glimpse its wonders and yet are trapped here by the speed of light." So well said

I'm no expert, but, it seems that the ultimate paradox of sending the messages back in time before the event happened only appears if you switch between the two frames of reference. Which you do (we are talking about material around 19 min of video). To explain, you mark the signal of supernova travelling from earth to the stl ship instantaneously as observed from the earth and then mark how the signal to switch the FTL transmitter travels from the stl ship to earth as observed by the stl ship. If you were to draw the signal lines corresponding to single observer only, they will almost overlap and be parallel. Given a slight time delay in the machine that receives and interprets the signal and sends the signal back (a computer constrained by the speed of light for example) the signal to switch off will be always slightly later. Causality violation will never occur from a point of view of a single observer and no-one would ever be able to experience it, including the machine that sends out the supernova signal and receives the switch off signal, unless they can be in two places at the same time and be able to switch between the two frames of reference freely.

The greatest explanation so far. I've been trying for months to understand this by reading forums and watching youtube videos. None were able to explain this. I still need to understand it more intuitively instead of through looking at lines, but this definitely opened my eyes. This is by far the best and most simply explained video so far on this. Thank you

"The cosmic speed limit, the speed of light is so diminutive compared to a galaxy. It almost seems like a cruel cosmic joke that the universe be arranged in such a way that we are able to look out and glimpse its wonders and yet are trapped here by the speed of light. Fated to only ever peer through the bars of our cosmic prison and dream." -- This is so beautifully spoken...

I like how Terry Pratchett said it better than the way Hawking did: Everything that happens, stays happened.

There's a great scifi series on a subreddit where humans are using C+ canons that send projectiles using something akin to "slipspace" to travel faster than light to target, and in universe from the target's perspective they get hit before the canons are even fired.

This video is amazing. Thank you for this simple explanation of such complex issues. I have discussed your diagrams with a couple of colleagues last night and we had an amazing time 😊

In the Halo extended lore (books and etc), their use of slipspace creates time paradoxes like, constantly. It's not uncommon for a ship to arrive at it's destination hours, days, or WEEKS before it left. And everyone's collective reaction to the existence of these paradoxes is just to kinda shrug, say "hey man, don't worry about it too much," and move on

I landed at the same "strict rules" conclusion back in 2007 when designing a sci-fi setting with FTL. I borrowed a bit from Douglas Adams and ended up with a version similar to one you hinted at. That any attempts to perform an action which would result in a paradox would be met with increasingly unlikely events to prevent it from occurring in the first place. Thus, before sending any FTL comms, or engaging in certain kinds of travel, you have to draw the light cones and think through the implications as shown in your video. Thanks for putting this together. It was nice to see someone think through the same things and tie it into a neat package.

Thank you Professor, very interesting. I myself think that the only reason we even discuss FTL travel is because SF writers had to 'invent' it in order to write space travel stories. One thing: I believe you pronounced the word *albeit* as 'al-bite'. Actually albeit is simply a contraction of 'although be it' or 'although it be', and so is correctly pronounced *all-be-it*.

I enjoy that you are actually including the possibility of breaking the universe in this video. That is why we stopped increasing speed, in my warp engine space ship.

Omg this diagram finally explained why and how space and time are connected. Thank you so much. I always thought I understood this concept but I was just repeating info not fully grasping it.

Hiya, aerospace engineering grad student here! This seems really well-researched, and yes, this _is_ an effect that happens exactly as you say - and it's also not time travel. Not in the way we conventionally think of it, anyway. This model is actually referring to _information_ travel, which is surprisingly pretty different! And no, even if you switched the FTL signal to, say, a person traveling FTL to tell the Vegans (lol vegans XD), everything still holds up to how we understand relativity. This is because this thought experiment doesn't factor in the *quantum effects of information.* Take a pair of electrons, for example - let's make these two electrons quantum-entangled (something that can actually happen!), which is a fancy way of saying that their properties are connected and shared - when one electron does something, so does the other. We have experimentally proven that, when one electron's spin flips, so does the other - _instantaneously._ Which shouldn't be possible, so long as we assume everything is capped at the speed of light. AND this happens regardless of the electron pair's distance from one another. So in theory, if we separated these two entangled electrons across the entire Milky Way, then flipped one, the other would also flip at the exact same moment as the first. This is because with _information_ travel, there's no light-speed limit to be found - no speed limit at all, really. So when one electron flips, the information of that flip _instantly_ travels to the other electron, and so it flips at the exact same time. Crazy, right? All this just to say that, according to quantum physics, information is not bound to the rules of relativity, in regards to both space AND time. This is exactly what happens in this thought experiment - due to the nature of the different axes of space, the information onboard the STL ship comes in all jumbled and in the wrong order, but because information doesn't actually have a given speed limit (the entangled electrons are proof of this), nothing in relativity is broken! The rest of the universe follows the horizontal axis (mostly), and causality remains unbroken - since the space axis is relative to the observer, the *perspective of the order of events can change* because _information has no given speed limit,_ it's only limited by how it's perceived - so the events themselves still happen exactly in the order they happen. The line parallel with the space axis, traveling up and down, is really an _information perception line._ Think about it this way - forget the signal. What if you had a ship that traveled at exactly the speed of light? Both its time and space axis would be at 45 degrees, and thus its perception line would also be at 45 degrees. In that frame of reference, all three events - supernova X, Earth observation of X, and Vega observation of X - would happen at the exact same time. And what if we add back in the signal, and the ship was an FTL ship? Flip the STL ship line and the STL space axis line at <a href="#" class="seekto" data-time="887">14:47</a>, and we're FTL! The perceived (note: _perceived_ ) order gets _really_ janky with this example - first, the Vegans receive the warning from Earth; then the Vegans see X; then Earth sees X; then X happens. It's almost backwards! But that's okay, because *information - and thus our perception of that information - can arrive in whatever order it wants, or rather, in the order that the frame of reference allows.* No time travel, just information travel. Just thought I should mention that, to alleviate the confusion! Physics, sadly, just _really_ doesn't like actual, real time travel. (My inner Doctor Who fan is crying) Edit: Whoopsie, so I brought this post by my thesis advisor, aaand turns out I may be just a _wee_ bit absolutely incorrect about how transmission of information via quantum entanglement works. Say you have a pair of entangled electrons that you've measured to have a net spin of 0. If you measure one electron's spin to be some value x, due to quantum entanglement, the other electron's spin must be -x. Simple enough, right? All entanglement says is that mutually shared info is conserved. _Technically_ it means you also instantly know that the other electron's spin is some value -x once you measure the first electron to be spin x, but the pitfall for many people (including myself, sadly) is extending this logic to the _transmission_ of information. Just because an electron is entangled with another doesn't mean flipping that electron will have an instant effect on the other. Transmission of information is, much like everything else in the universe, bound to the speed of light. Physically flip an electron, and the other electron will flip after an appropriate amount of time, NOT instantly. (Note that this also is in an ideal setting, where spin only happens along a single axis - normal electrons can have spin along any axis they want, which has all sorts of brain-breaking issues that I will NOT try and summarize for both your and my sanity.) Having said that, though, the logic of the information perception line still holds true to a degree. Proper FTL travel doesn't yet exist, so we can't properly test the effects that FTL might have on causality. The thought experiment proposed in this video calls into question some of the issues FTL might have, but this post is more calling into question the claim that what's happening is time travel. An error I made was assuming the information in this setting was quantum information, which makes no sense since this isn't really a quantum system! You find quantum info in a quantum system, which this isn't, so the information perception line is really just the perception of normal, tangible information. (And again, quantum info like everything else is bound to the speed of light. Just pointing out another error I made.) And yes, it still looks like causality is being broken, but still only from an information standpoint. Events still carry on as they do, it's just the order of _detection_ of events that's getting weird. Which is totally fine! Harking back to the entangled electrons, if we separate the pair far enough and make enough observations in a second, communication via the speed of light would take longer than the interval between observations, meaning you can find out the other entangled electron's spin faster than the other side could tell you what that spin is. So in a bit of a backwards way to what I said earlier, information _still_ finds cheeky ways of "beating" the speed of light without actually beating the speed of light. If information can do that, then there's no reason why this doesn't extend further ie. to this thought experiment. Information gets wonky, but we already know that's okay. No time paradoxes here! To be fully honest here, I ain't an expert in this field - I'm a hands-on build stuff kinda guy, the stuff discussed in both what I've said as well as in this video are only tangentially related to what I study. Thanks so much to all the people who've (politely) criticized my errors - y'all were the reason why I brought this to my thesis advisor in the first place. Science is all about correcting incorrect assumptions, so thanks to all of y'all for setting me straight! And feel free to point out any other errors I've made in this edit - there's only so far proofreading will get you lol

Revisting this. Professor, I just saw an article featuring your terrascope idea, featuring you, of course 😊. I was so excited for you

Always a GREAT day when KZfaq dings you because there is a new Cool Worlds!! 🛎 👍

Yet again you combine scientific explanation with a thoughtful and beautiful message. Thanks for one day deciding to start doing these videos, they mean a lot to me.

Great video. Speed of “thought” as form of FTL travel? Perhaps currently the only way. Also, love Hawkings ideas that time paradox’s are impossible.

Maybe I'm vastly misunderstanding things, but I feel like no matter what you do you'd be unable to break causality. Time is moving forward for everyone, just at different speeds, right? So no matter what you do(even sending a signal FTL) you'd be just unable to break causality. Maybe this answers that "does light travel faster in one direction" question(there was a Veritasium episode on this idea), so in this case trying to break causality would actually "slow" the speed of light to preserve causality. So your message, to you(the STL ship in the diagram), is still going FTL, but to Earth your message would be STL and they'd get your "turn off FTL communications message" *after* sending their first message. I guarantee my logic here would make Stephen Hawking froth in rage, but my college dropout brain refuses to accept causality could ever be broken.

What is most beautiful about this video - is actually what it has done to the comments section. Look at all the wonder, the questions, the curiosity, the debate. All these wonderful human beings trying to discover - this is what I love most about humanity, we're all in this thing together :)

If FTL is impossible, the upside is that the possibility of aliens attacking would be quite low.

What if for the reply signal that gets sent back (for the Supernova FTL Warning example), could we potentially just calculate the point in time/space where Earth would be, and send a signal with a specified frequency to travel the exact speed needed to meet that calculated point?

It's amazing how slow you plan to go faster than light. I have other things to do. If I have time, when I'm finished goofing off, I might check in to see if you made it to light speed.

Cosmological and chronological paradoxes are so interesting, rather enjoyed listening to this more than I'd expected.

The direction of the return ftl message from the stl ship is unexplained here. I would love to know the reason for that, seems like the most important part. Wonderful vid, very informative and easy to follow!

Sorry to double-post; but this is one of the best videos on this subject. I often discuss why FTL communication alone can create paradoxes; but it is a tough concept to internalize so I have to go back and re-think it through. (Either by watching a video like this or drawing my own space-time diagram.) Speaking or spacetime diagrams, maybe you can siimplify it. Perhaps you can consider just "earth" and the sub-light ship communicating instantaneously (FTL.) Instead of a message and response becoming flipped, consider a continuous "open channel" (like a real-time phone call with both the home planet and the ship without ever hanging up.) Since time goes slower for the ship right from the beginning anything said from one will be heard from the other in opposite order, with the difference between the two getting greater and greater. (As an aside, I suppose on Earth the voice from the ship should sound in slow motion, while the vocals from earth should sound speeded up on the ship.. this is incidental, but it demonstrates since the vocals coming from the earth will be super fast containing much more information why it will appear to be from the *future* from the ship's perspective. Perhaps have the earth to ship channel constantly reading the news....the crew of the ship will hear the news more and more from the "future." I put that in quotes since it's cool from the ship's perspective. It's only the "future" if the ship then instantaneously relays that information back to Earth. ) Thus the time difference between call and response will continually increase as the distance/time between the two increases.

By far best explanation compared to all others. Great job. Could be perfect if at <a href="#" class="seekto" data-time="870">14:30</a> (most frequently played viewer likely replying because it was a bit confusing) if you just explained more why the 45 degree flip dotted line for STL rather than mention to refer to a previous video for that understanding. Still good job.

Congratulations, you had my complete attention to the entire 25 minutes. Very well done video and explanation. Super interesting

I like how he predicted every point where I got confused or skeptical and delivered a good answer without me ever asking anything lol About the talk in the end about exploration without FTL, it was quite poetic, but individuals can actually experience it one day and travel to many stars, considering there is no barrier in the laws of physics that say living things can't last for billions of years. More than that, the way in which time is perceived can be drastically modified, where a million years travel can feel like a mere hour. Just imagining human-like consciousness in a digital substrate is enough to see how this things are possible

Great video and it really got me thinking! There is one thing I don't understand though, and would love to hear an explanation from a physics student or a professor. Which is this: how can the STL ship send an FTL message to Earth's past? This is how my non-physics brain perceives the situation and what I (think I) understand: 1) Time is relative for both the Earth and the STL ship 2) Time on STL ship ticks slower since they're moving closer to the speed of light. They are moving towards Vega and away from Earth and the supernova. Hence it makes sense why the first thing they see is "Vega receives message" in the previous diagram. 3) While time has slowed down for the FTL ship, time ticks forward for those on Earth. 4) Now let's assume that 1000 years have passed since STL ship has left Earth and that's when the supernova explosion was detected by Earthlings. This means when Earth sends the FTL message and STL ship receives it instantly, 1000 years might have passed on earth while only 1 year might have passed for the STL ship's crew, depending on their speed. So far so good. (5) And this is the bit that messes with my head. When STL crew responds to that message with another instantaneous FTL message to Earth - how is that going in the past exactly? 1000+ years have already passed on Earth when the STL ship responds instantaneously, meaning Earthlings should've received the response AFTER they sent the message in the first place. While Earth might looks like it's stuck in the past to the STL ship, in reality time has progressed a lot further than it did on the ship. The Earth itself is not in the past. Thanks in advance for your help. I hope someone can clearly explain how STL's FTL message ends up in Earth's past (with examples if possible). Thanks for your patience with my limited knowledge of physics!

If you’ve ever listened to people’s near death experiences they’ll often times describe going to the light and then time no longer being a concept, as if everything is happening all at once.

Let's start perhaps with a more modest goal: Alcubierre-style drive that targets STL flight instead of FTL. Even that would be a tremendous step forward for our civilization.

You're such a great human! Thank you for all your content!

at <a href="#" class="seekto" data-time="1020">17:00</a>, the video illustrates how the "STL ship's time axis" should be vertical (plus, then FTL works again, according to this model)

It would've been useful to see that diagram from the STL ship's perspective, since it's not very clear why their reply travels at that angle

Attempting the impossible almost always brings great discoveries even if it's not the one that is being sought

Great vid bud, very much enjoyed it! 👍

This is an amazing video and I love the breakdown and diagram! I do have one part though that is preventing me from fully grokking this concept, possibly the most significant element required for me to understand the time paradox. Around <a href="#" class="seekto" data-time="1090">18:10</a> it’s not explained why the FTL message from the STL ship goes backwards in time. The space component makes sense. But I assume the response transmission to turn off the FTL transmitter would go UP and to the left, not down and to the left. I assume there’s a reason but I don’t feel like that fundamental piece was thoroughly explained. Love the work done, keep doing great work, just want to understand that piece more. Thanks :)

respect to all the cameramen who time travelled into the past to bring us footage of all their FTL ships for use in this video

I'm 30+ sitting here at <a href="#" class="seekto" data-time="208">3:28</a>am and have just learned through that graph, how their theories come about. I could listen you talk all day and will definitely sub to your channel ❤

<a href="#" class="seekto" data-time="918">15:18</a> If we are looking at things from the ship's crews' perspective, how can you say that the first thing the crew perceives is Vega receiving the message from Earth? How did that information get from Vega to the ship? Was it instantaneous? Doesn't this information take time to travel to the ship from Vega? Yes, the time line has reached Vega, but it hasn't reached the ship yet. In fact, it appears that the ship learns about the message from Earth to Vega when the ship arrives at Vega (this might be an artifact of the speed of the ship, and might not be true for a different speed). More importantly, according to your timeline, the STL ship thinks Vega has received the message from Earth BEFORE THE SHIP HAS LAUNCHED. <a href="#" class="seekto" data-time="1091">18:11</a> Justify the world line for the return message from the ship. No matter how I look at it, the message from the ship back to Earth arrives later, not earlier. I don't see any way to get your reply world line from any of the other lines you've drawn.

Even if FTL is impossible things like Alcubierre drive and wormholes could , hypothetically, still be used for slower-than-light or light-speed travel. STL or light-speed wormholes might also be useful as makeshift pocket dimensions, since the throat would have to be longer or the same length as the distance between the two mouths in normal space. They could also be used for uninterceptable communication

Phenomenal job of explanation & presenting in a minimalistic way 👏🏻👏🏻👏🏻👏🏻👏🏻

I think as soon as something like FTL is achieved, we'll soon learn that there is some other, infinitely stranger arbitrary limitation way beyond our grasp that we could never have even conceived of before. I have dreams about it all the time, since I was a child in fact.

The speed of light should really be taught as the speed of causality. The speed of light is an incidental stenographer of the speed of causality.

so my question here is at around <a href="#" class="seekto" data-time="1090">18:10</a> you're demonstrating what happens if the STL ship intercepts the FTL transmission, then sends a transmission back saying to "turn off FTL Transmission", what rule applying says that the returned transmission must move backwards in time? Why would it not move to upper position of the diagram of which case Earth would receive that transmission before Vega see's the Supernova keeping the order of causalities in line? Why must the returned transmission from the STL ship back to Earth be moving backwards in time?

Don’t take this wrong but the style of this video’s cover is really like 3b1b which is one of my favorite channel, and also thank you to make contribution to spread the knowledge and explaining everything to us😂

I'm having a lot of difficulty wrapping my head around some things here. For example, why is the space axis a mirror-flip across the null line of the world line? For the "stationary" earth I get that it would look like a mirror-flip, but why is it? Also, when the transmission is sent from the STL ship after receiving the earth transmission, why is the slope negative? I feel like having this side-by-side with a similar diagram for the STL ship's perspective (with its world line being vertical, and the others being angled) would help clear things up... Like, I get that there's some consideration here for time dilatation, but wouldn't that be bypassed too, as using something like the Alcubierre drive, the object is not actually moving FTL, just the space it resides in is, so it wouldn't suffer time dilatation... I'm just getting confused.

Your written script and voice work is top class, man. Documentary level for me, especially for a subject matter that I find intriguing.

What a fantastic misunderstanding of the subject. Glorious video, classic KZfaq.

Great work explaining this causality breaking phenomenon, the visual and the diagram definitely shed some light on this mystery for me. Thanks. Here is my take on this thought experiment: the crew was traveling STL above the null line and the time travel paradox hinged on the assumption that Earth and Vega remained stationary in space while the crew was traveling through space-time. I think we get the paradox because of the assumption that Earth and Vega are stationary in space. Do we need to further assume the crew ship travels faster before Earth and Vega are set in motion through space? Is that even possible if the crew is traveling STL? Will we get the same time paradox if all three are in motion through space? Do the laws of physic allow freezing Earth and Vega through space while traveling STL? I'm just curious and trying to stay thoughtful. Thanks for the video, I truly enjoyed it.

Best explanation of time travel paradoxes I've seen in a long time, thank you for this! I feel so amazed that on one hand we can theorize and explain stuff like this yet a lot of people will still doubt that we ever went to the moon.

Have you done the math with the actual Lorentz Transform equations? In the case of instantaneous travel, there are 3 events that occur at different locations and different times according to the two different reference frames. A message is sent from Earth the the STL ship and then back to earth both via FTL. It is absolutely vital in this situation to define the first two controls: The Earth time + location the message was sent, and the STL time + location the message was received. Once these controls are put in place, the diagram as shown no longer works (FTL breaks the rules of this diagram). However, the underlying Lorentz Transform equations are still valid. You will find an observer at a distance can witness events that are out of place, but NO message can be sent by any means before the origin, even with instantaneous travel! I have done the math several times with the correct controls, and Sabine Hossenfelder released a video that agrees with this finding.

<a href="#" class="seekto" data-time="894">14:54</a> Dont you have to start at the space line of the STL space axis like you did in your world time example? Vega wouldnt receive the warning from the ships perspective at this moment. It would know about the event, once the ship lands on vega. Wich makes sense since more time has passed in both systems. And why would the message travel backwards in time but forward in space once the STL ship responds?

The universe doesn't care if it makes sense to us.

Well this is the best explanation I've seen that explains why FTL will break causality. Every other show or channel just mentions that a violation will happen; you actually break it down and explain it clearly step-by-step. Amazing. You deserve a much wider audience. I will start referring others to your channel.

Surely the ‘paradox’ stems from the problem that your graphical representation ‘calculated’ the outgoing ‘instantaneous transmission’ from the Earth’s frame-of-reference, but the incoming ‘instantaneous transmission’ from the STL ship’s frame-of-reference. I would have thought that two instantaneous transmissions from A to B and from B to A (both sent at exactly the same time) have to follow the same path through space-time when modelled in a single frame-of-reference. Which would mean that both transmissions lines should either be parallel to the Earth’s time axis or to the STL ship’s time axis, depending upon which observer is measuring the path through space-time.

Does anyone have a link/article/something to further explain why the space axis is the reflection of the time axis over 45 degree (c-line)?

I wish every video was so capturing and beautifully made - just epic

Outstanding! FTL was always a dream since watching Star Trek as a kid. The fact that we can glimpse these wonders of the universe as water filled meat sacks is truly amazing. Even if it isn’t possible, I appreciate that logic as to why is isn’t possible. Space is big. We’re living in an age of high definition discovery.

That was awesome,, answered a question I've had a difficulty conceiving for so long.. it now makes sense and as always opens the door to more questions. Great video and thankyou very much..

you didn't explain why the STL ships signal would go back in time.

Despite David's simplified explanation, the concept of space-time paradoxes continues to confound and overwhelm my understanding. Nevertheless, It's so cool..

I always love the very grounding and philosophical thoughts proposed in these videos along with the theory. Really helps to place the science and the importance of these studies in a broader sense and why or why not humanity should pursue them.

I would posit that it is possible it's just all about frames of reference. You would not be able to affect anything in your personal referential past. You could observe it, but not change it. I think the diagram is off in using the frame of reference for the STL ship as the "speed" of their FTL message would be significantly "faster" than the message from Earth. The correction for this means that their message would NOT arrive prior to that of the sent message. (On the graph their message would appear to them (could they see the graph) to curve upward past the message point. Using star trek terms if you fired off a message at warp 1 its not going to travel at (warp 1 + full impulse) simply because you were going at full impulse. Basically this graph "forgets" that for all of the pink FTL lines, the straight "space" line is not straight. For them it is a curve, so if you factor that in and the flatten it back out it shouldn't violate causality. I am probably wrong somewhere, it's 2 in the morning...

The engines don't move the ship, the ship stays where it is and the engines move the universe around it!

<a href="#" class="seekto" data-time="1089">18:09</a> why would the STL ship's message answer go back that way on the diagram? I don't get it at all. It's very confusing because there were no example of someone answering back without FTL shenanigans.

If you moved instantaneously from earth to vega, and then told someone - to instantaneously go to earth, and tell them to shut off the instantaneous transporter, they'd arrive essentially the moment you left. That's significantly faster than light speed and there's no causal issue. The whole reason the space line is the time line reflected by the null line is Because we assume the fastest speed is the speed of light, that's an emergent property of the assumption, and any relativistic effects assumed to also be reflected are affected by that original assumption. If you bend or break space itself to accomplish moving subluminally from point A to point B in a shorter time than light could travel that's fine - if difficult, but it wouldn't allow for paradoxes to arise, you're moving slower than light in your own reference frame, from the reference frame of your starting and ending locations - it's as if they are closer not as if you are faster. If you traveled through space more traditionally as you got close to the speed of light your physical and nuclear properties slow until you reach light speed and they halt, you couldn't perceive a message arriving at your location at this speed and even if you kept a record it wouldn't be reacted to until you reached your destination, upon which even sending the message back at the same absurd speed wouldn't arrive back to earth before it was sent. There's also the issue of spreading out if you behave like a wave at that speed, becoming red shifted as space expands with you moving through it, and if fermions and bosons behave the same way through space at those speeds - you might arrive out of sync in a catastrophic way, unless your beginning and ending points are specific distances away - regardless of how long it took you'd eventually find such a place, and even then they'd need some marvel of engineering to slow you down or put you back together once you arrived. Your mechanical interactions would stop entirely as two objects moving in the same direction at the same speed never collide, no nuclear interaction beyond perhaps making you more or less energetic in difficult to predict ways, the magnetic components would just cycle as you travel hopefully arriving in the right orientation and not becoming a tangled mess. If Everything lined up Just right, you'd arrive after experiencing no time pass yourself, it feels instantaneous to the traveler, and that's only moving At the speed of light. If you moved somehow faster - which is as absurd as constructing a machine Out of photons to propel photons faster - you can't experience less than nothing happening.

It’s actually really easy to go faster than light, just make a big ball of light and attach a couple rockets to it

How would the stl ship receive/perceive info about Vega receiving a ftl message? Are they just receiving earths ftl message to Vega? because on the diagram the ftl message axis intersects with the stl ships axis after Vega receiving the message.

This video made me think of a really enjoyable sci-fi novel I once read, called "The Depths of Time". In it, humanity has the ability to use artificial wormholes to traverse the galaxy. These wormholes *also* traverse time. Since they only have STL ships, they travel at sublight speeds (with the entire crew/passengers in stasis) for upwards of say, 100 years to the 'up' end of a wormhole, traverse through it which takes them a great distance and 200 years into the past, then travel at sublight for another 100 years (plus maybe a couple weeks) to their destination. Thus, arriving thousands of light years away only two weeks after they left. To enforce against time paradoxes, there is a highly armed and technological 'guard dog' type of group that protects these wormholes, and ships that use them have their communication systems highly encrypted/deactivated so they cannot communicate with the outside universe while they are in 'their own past'. It's also interesting engineering, as although the ships may have chronologically only been in service for a few decades, they may have tens of thousands of years of travel on their internal chronometer...

Damn - these shows are amazing. I love the philosophy components and the human impact of cosmic questions.

you can't turn ftl message wordline to stl ship frame refference(because ftl message is still absolute to the universe time-space frame) so when stl ship receive message its reply is inverse to receiving line so reply is receive at earth after. And that dashed line of stl is only time reference for in-ship time so it is moveable(alongside time axis) and that way, where it cross ship's full line is when something happens in crew perspective time. So when they arrive on vega and get the information from ftl ship it appears on dashed line on crossing with vega's full line. So no paradox occure!!

Good video I can't comprehend all the access of time and faster than light travel right now cuz I'm nine beers under but what I suggest is at the time that we do have speed of light or faster than the speed of light we should make a first travel Two planet Mars, then speed of light probably 8 minutes or 8 minutes back and then after that ( Tomorrow's faster than light right light speed) travel to the 7th or 8th planet out, faster and light and back probably 15 minutes or 20 minutes and back, that way we can get a coordinates of understanding of all that you're talking about before we actually go out to other star systems!

<a href="#" class="seekto" data-time="1091">18:11</a> "Bizarrely, it would follow a world line like this." - Would be great if you can elaborate more on what makes you draw the line that way.

Edit: Cleaned it up. As others have mentioned, the only constraint necessary for a vector to have a >= T (Time) value. The problem is that T and S axis are different for different frames of reference. The one frame can have a vector with positive T (maintaining a dot product == C), but be a negative T vector (or dot product C) when translated to a different frame of reference. I think then the problem, all vectors having a positive T (and vector dot product == C), would be solved if there was an absolute frame of reference. A possibility frame would be the expansion of the universe. If all vectors are then constrained to having a positive T (and dot product of C) on the universal frame, regardless if a vector from one frame translates into a negative T vector in another. The universal constraints would then not be violated. That also means that "time travel" would really only be within a local frame, not the universal frame. Local paradoxes resolve on the Universal Frame. I think that makes sense. And hopefully I used the correct terms; my math is old and shaky. IANAP (I am not a physicist)

What if the acceleration after light speed rather than adds more speed causes a bigger time dilation that preserves causality by from your prespective making everyone elses time pass faster?

If a system like an FTL communication system did exist, you could probably avoid the paradoxes by having unique communication "channels" where only certain references frames could interact with it, or just not have FTL communication between STL ships and main communication systems. You could also probably analyse what ships are travelling based on missions you're running and you could analyse possible paradox creating courses of events and avoid them. What would happen if you ran the same thought experiment but with an FTL ship?

I love watching this channel. I have such a longing for knowledge of the universe, space and all the theoretical studies and possibilities they potentially propound. I feel like I'm learning with every video, yet after each one ends, I feel more stupid than before I started.

I think a possible sollution to the time travel paradox is a system like we have seen it in the show Dark. The reason why you cannot change anything by traveling through time is because the events always included you traveling in the past. Meaning that the ship sending back the order to turn out ftl communication happened in the original time line as well, and was there ignored. So, the idea that time paradoxes are impossible is that actions of time travel always happened and this cannot change the outcome.

At <a href="#" class="seekto" data-time="817">13:37</a> you started the STL line/journey before the Earth sees the Supernova X event, This means that it is absolutely normal for them to learn that Vega received the warning becasue they started from Earth before seeing the event. They will learn about Vega receiving warning only after they reach Vega and it is an event of the past for the ones on STL line when they reach Vega. For example: 1. I started from my home to office. 2. Burglars break into my home. 3. My neighbor makes a phone call to me about the event 4. I learn that this happened This doesn't mean I learnt about it before happening. It means that I started from home before it happened.

I’m struggling to understand why you placed the space axis for the STL ship, if we created a new chart with just them line it would be well below the null line no? It was at a very acute angle

Sir, I only found out about you less than a month ago but have almost instantly became obsessed with your content. Keep it up man, I love everything you put out.

From the messages point of view, even if it was travelling instantly it still has to travel "through" all the light emitted from the destination. If its destination is 1 light year away, while travelling towards it it will see the destination experiencing a full year. If it then turns around and looks at the source it will be a year in the past from when it left but if it immediately heads back it will not arrive a year in the past it will see the source experiencing a year in an instant and arrive at or after the time it originally left.

tbf, being able to just go the speed of light or near it would be pretty good too, it might not make us able to travel to other galaxies, but the nearest stars get as low as 4 light years away, being able to get to another solar system in a lifetime would still be game changing

Awesome video, I love it. So the 0° - 90° diagram with null line on 45° is just for causality-breaking demonstration purposes. The 'real-situation' diagram would be with null line on 90° line, where no time passes when travelling at the speed of light. (I guess this also goes hand in hand with 'photons do not experience time' theories). If you were to (hypothetically) somehow go faster then speed of light (on this 'real-situation' diagram), it would be 91° angle (or higher) and you're automatically going back in time on vertical time axis. Interesting. The simulation theory is seriously starting to make more and more sense to me by each new understanding/discovery we make, and I am now wondering if time is just a computational power of this Universe. Speed by which matter/energy interactions are calculated and 'rendered'. The SLOWER you go through space, faster you go in time (higher frame rate), since there is less things to calculate (less total matter/energy interactions). The FASTER you go through space, slower you go in time (forcibly), since you're touching a lot of surroundings and all of it needs to be calculated. So there is a cap, an upper-limit on calculation. If you were to break it, you'd reach points in space for which interaction calculations haven't been calculated yet (again, you travelled to past, in a way). Damn.

My conjecture is that when you are moving faster than the speed of light, regardless of the means of doing so, you are not actually moving along a spacial path that enables time travel paradoxes. The equations of relativity actually solve to show you are moving along an imaginary (think the number i) time axis if you were somehow moving locally faster than the speed of light. That said, if you are moving space faster than the speed of light, you, yourself, are not moving faster than light. Space time is not actually distorted for you enabling time travel paradoxes due to your locally subliminal speeds. In fact, I would go so far as to say that if time travel paradoxes happened due to spacial distortions that happen faster than light speed, then the universe would already be experiencing paradoxes, given that universal expansion happens faster than light speed. We literally *observe* it happening FTL. Notably, the universe does not contain time travel paradoxes right now. That alone should tell us that relativity, albeit is a smart idea, is clearly lacking the proper answers at extreme conditions such as FTL (not to mention inside of black holes). If time travel paradoxes are to exist, it’s possible that the universe simply “overwrites” both states into existence at the same time enabling a universal memory of both states, which would locally enable humans to realize that the time travel “paradox” exists and simply do the effect that enables the cause. That is, for the transmitter message, the universe would enable it to happen but it would simply ignore its effect on itself. So the message would still transmit because the universe ignores the effect of the message to shut itself off before it even started. Another possibility is that since the FTL message would not be continuously actually tied to the spatial line of the STL ship, it would simply “readjust” to move along its proper spatial line as determined by a non-inertial frame of reference and would just move diagonally towards the earth into the future. The only people who would perceive it as reaching earth first would be the people aboard the ship, and they would simply be observing something they cannot logically determine or they would simply actually observe the FTL travel happening along the non-inertial path and thusly reaching earth in the future. As to why that would mathematically happen? I refer back to Einstein’s equations not properly working in extreme situations, just like Newton’s didn’t work in another set of extreme situations leading to Einstein’s equations.

Thank you for this lesson! I finally have a slightly better grasp of 'world line' diagrams. I did't realize, or remember, that all "C"/ Light Speed lines are 45degrees. That helps. Now, I'm gonna look at a nice sunset to rest my brain!!

I have an affinity for how this gentleman explain science jargon in elucidating terms to the lay person and makes it also both profoundly educational and entertaining. He's never ever boring.

Ok. I'm no scientist or mathematician so please excuse my clumsy effort. But there seem to be a few problems with this logic/diagram/explanation. Maybe someone can point out my errors. 1. Using the ship's space axis line or its angle as the base to measure the sequence of events seem false. While it may seem to the crew that the order is different, it doesn't change it in the "outside" world where they are not moving at the speed the ship is traveling. This seems like someone traveling in a bullet train looking out the window saying the world is so blurry. While it may appear that way to the person on the train, the objective world outside doesn't change to fit that observation. When measuring the effect of change or sequence of events in the outside world, you must use their own space axis, which is still horizontal in this diagram model. Then, the sequence of events still make sense. 2. Reply from the ship back to earth seems completely wrong. Assuming the speed of the FTL message is constant, why is the line from the ship to earth at a different angle? Yet, another even bigger problem is the flow of time. Based on the diagram, the time flows upwards along the Y-axis. Then, the message from the ship to earth should also go upward at an angle reflected about the horizontal line. So if the original FTL from earth to ship was at an 30 degree angle (indicating it is faster than the speed of light at 45 degrees) measured from horizontal line on the right side, then the FTL from ship to earth should be 30 degrees (again indicating it is faster than the speed of light at 45 degrees) from the horizontal but from the left side. This is because again, the objective time still flows upward along the Y-axis. The line drawn in the diagram noting the message from the ship to earth literally says the message is traveling backward in time.

Isn't the STL line off? The slower it goes the more vertical it will be, right? But then, the mirroring at the speed of light would be more extreme, to a point where the angle becomes zero, if the STL ship does not move at all, hence the time slice would be horizontal too. The message back, seems to travel backward in time in any reference system. Why? Just because it is drawn this way? Shouldn't it be angled up, and everything is restored? Looks to me, that in addition like the space/time coordinates of the STL ship are confused with that of Earth and Vega. Or vice versa and this causes the paradox. Confused.

This is the first video I watch of you and I am amazed by the quality of the edit and the way you explain these concepts. Thank you so much :)