well, the word 'lux' is related to the Greek word 'leukos', which is usually translated as "white", but also covers the meaning of "bright," or "light" as in "a light colour"; so, it's not totally off 🙂
so how fast is infinite speed the pink line needed to travel back in time, just before it becomes infinite? also what does it mean moving faster than light but still travelling forwards in time,the space between the yellow line and pink infinity speed?
"Math always gives us an answer, even if our question isn't about reality." -- Nick Lucid May be one of the best math/physics quotes I've heard in a while. I don't know if he was quoting someone else, though.
@@ScienceAsylum The way I always think about it is that math is a model. No numbers are "real", just useful to describe stuff, which makes irrational numbers, imaginary ones, quaternions, etc. just as real. Sometimes that does make me wonder if some mathematical equations we use as models are just extremely precise rather than exact. You probably know more about that than I do though.
A fact that is generally overlooked about "time move slower the faster you go", its thats only true relative to another frame of reference. The electron in question will always perceive its time passisng normally, a second will always last a second for it, but it will expercience the outside world to move way faster and distances shirinking
It's like trying to get ready to go out somewhere when one has ADHD, time goes faster than I thought it would once I try to have a shower and get dried then dressed before I leave.
An observer moving at large fractions of the speed of light will observe their own time passing as normal, will observe the rest of the universe as moving slower in time, and having been length contracted in the direction of motion. Because from the perspective of the observer that's moving, it's everything else that's moving.
@@MarcusM-bw9nuYou should watch again and take the above comment in mind. Then you'll probably grasp what happens the right way. As an example of such relativistic phenomena, let's see what happens to a cosmic ray hitting our atmosphere. The atmosphere is about 100 Km. thick. When struck by a cosmic ray (a particle from outer space at a speed close to that of light), it disintegrates in a cascade of particles that also disintegrate spontaneously or on further collisions in the upper atmosphere. One of the products of such disintegration is muons. Muons have a short life, only some microseconds, so that they can only travel a few kilometres before spontaneously disintegrating. But they reach the surface! For muons from cosmic rays, our atmosphere is not 100 but about 10 Km. thick, and it rushes past the muon at a speed much higher than that of the cosmic ray due to time dilation. So, the muon has time enough to reach the surface: its clock is slowed, as 'seen' by us. For the muon, less than the allowed lifetime is required to traverse the whole of our atmosphere's thickness.
It's common to use the Special Relativistic equation in hyperbolic form: c²t² - x² = c²τ² But it makes more sense to subtract the negative term from both sides to express it in Pythagorean form: c²t² = c²τ² + x² Divide both sides by t² to get c² = c²τ²/t² + x²/t² That's more relevant when discussing "speed" through 4-dimensional spacetime, because τ/t is the traveler's _rate of aging_ from the perspective of a stationary observer and x/t is the traveler's _speed through 3-dimensional space_ from the perspective of the stationary observer. From those two terms, one can deduce the traveler's speed through 4-dimensional Minkowski spacetime, from the perspective of the stationary observer. The c² coefficient in the c²τ²/t² term is the conversion factor between the units of time & length, for the two "speeds" (rate of aging and speed through 3-d space). Since units are arbitrary, they could be chosen so that c=1: c² = τ²/t² + x²/t² It's a Pythagorean equation, where the square of a right triangle's hypotenuse equals the sum of the squares of the triangle's other two sides. In this case, the hypotenuse is the speed of the traveler through 4-dimensional Minkowski spacetime. (Minkowski spacetime has its time dimension orthogonal to each spatial dimension, which means the triangle is a right triangle.) So the square root of the left side is the traveler's speed through Minkowski spacetime, and it equals c, the same as the speed of light through 3-dimensional space. (And it equals 1 in the appropriate units of time & length.) The equation works for any kind of traveler, including light, and it presumably also works for tachyons. Everything travels at speed c through Minkowski spacetime. The equation tells us the rate of aging of a tachyon is imaginary, the square root of a negative number. But it's unclear whether aging at an imaginary rate has a physical meaning, so it might be impossible for tachyons to exist.
On paper, them tachyons come from the opposite diagonal quadrant of the Cartesian coordinates you are using, let's put speed on x and energy on y only. Well.. Massive particles will go up to less than c, normal ones. More energy, more speed but never c. Tachyons are the opposite. 🤔 so with our known observed reference, they are coming from infinite, lowering their energy to reach c but they can't, anyways, they can't get past c, but from the other side 🤔 How is that supposed to happen in the real world as we know it, we can't get past c from one side, tachyons can't from the other... 🤔 😞
@@misterlau5246 : I don't understand why you ask how tachyons' speed through 3-dimensional space can slow down to c. No one is saying it can. Because their 3-d speed is always greater than c, the equation implies their rate of aging can't change from imaginary to real. And regardless of 3-d speed, the equation says everything's 4-d speed is c.
You are a good science communicator. Many people do not make the distinction between maths and reality, although maths can give the best description of what is happening or will happen, the parameters need to be correct and precise, which a lot of people fail to see.
In the medical field, there is a specialty of medicine and of doctors called Cardiology. In that sub-field of the medical field, there is a term "bradycardia". Scientists and doctors love Greek words.
I was able to follow this to the end, but not to my satisfaction as my math brain is too limited. But this is the first time I've heard this subject covered comprehensively. It's a great service you're providing. Please keep doing the subjects YOU like!
Thank you. Since college (40 yrs back) I pondered what happens if you could go slower than STOP! My intuitive idea was backward time travel… Nick’s closing point is key to many maths revelations. Just because some idea can squeeze an equation out of a maths anomaly doesn’t mean it exists in our reality. Mathematicians generate some incredible meta concepts, but it takes a physicist to keep them grounded……Another brain stretcher was what would we see if Pi was a different value than 3.14…. It took me years to understand that one (ans: it warps things into an extra dimension. In curved spacetime for example pi is a bit bigger making you take longer to approach a mass than the geometric distance would seem…in this case that extra dimension is time. Pi is only the well known of irrational number on a flat surface…space time is not flat, even near Earth.
Indeed. I was a bit disappointed at the video’s conclusion, as “real” and “imaginary” numbers are just names that in the context of complex numbers do not mean what they ordinarily mean.
@@germansnowman Of course, that being said; even before the concept of complex numbers was invented, there was "math" applied to mysticism. "How many angels can dance on the head of a pin?" Etc.... The current conversation about applying "math" to tachyons is not dissimilar: Take something that has never actually been observed, assign a "value" to it, and plug that into an equation which really doesn't apply to the theoretical situation.
But they all must disappear (cancel out) before you can come up with an actual real world answer to any real world question. They do not exist in reality, only as a mathematical tool - an interim placeholder essentially.
@@germansnowman I think that was a pun. In case your username fits, "What I'm trying to say" is an English expression that means that what follows is related only loosely, by metaphor or example, but not literally. He was saying "Tachyons aren't literally imaginary (meaning #1), but they're imaginary (meaning #2)"
@@chuckoneill2023 I get your point. It’s just unfortunate that the common misconception about imaginary numbers being something “less than” real numbers was perpetuated by this otherwise great video.
I wish you would do a video on why we cannot use entangled particles to send messages faster than light. In UA-cam comments people often think we can. It would be great to be able to point them to your video. Now I have to explain to them that when we observe an entangled particle it takes on a random value, so we are just "sending" noise to the other particle. And even if we could send a signal, first you have to send many particles to a recipient at best at the speed of light. A couple of times commenters have been confused about Hawking radiation and I've been able to simply tell them to watch Science Asylum's video on Hawking radiation.
I love the deep dive into how FTL communication with tachyons could work. Math might not always describe reality, but it's always great for the imagination!
I love the channel, makes some pretty high end stuff accessible and entertaining. I like dabbling in the field, but so much reference material dives into the math. I like that you outline the proof, then get into the "so this is what it means". It's a rare talent. One of my favourite expressions about theorists is: "They could calculate the square root of a jam jar, but still not know how to open it." You sir, fly way above that,
Honestly, it was one of Robert Duncan McNeill's best performances on the show and the practical effects were amazing. It was just a terrible premise and it broke continuity. The _writing_ was the problem. I feel bad for everyone else who worked so hard on it.
@@ScienceAsylumI think they went with the idea of having a person's physical body existing at all points (at least along the line of travel)* at a given instant in time, doing wibbly wobbly timey wimey things to the subject's biology. Having observed the consequences they decided trying to recreate this with the whole ship was a bad idea (if it wasn't already). * They suggested that the ship could exist at every point in the universe at that instant, but glossed over that the ship's velocity was in a preferred direction so at any speed, be it infinite or plaid, it should still not reach points off to the side of the path travelled.
Thanks Nick - awesome explanations as usual. And it's good to come back to reality once in a while 😄On top of that, I think I will add "They're trapped in FTL" to my daily vocabulary! 😀
Honestly, it was one of Robert Duncan McNeill's best performances on the show and the practical effects were amazing. It was just a terrible premise and it broke continuity. The _writing_ was the problem. I feel bad for everyone else who worked so hard on it.
@@ScienceAsylumYeah, that's the thing with Star Trek. You can have amazing sci-fi sometimes, and then switch to very goofy and stupid at the drop of a hat. Sometimes within the same episode. It's good on the whole, but there are some very weird missteps.
I have a big multilayer question for you. In your "what if you were made of light" video, you said that photons experience 0 time, as well as so much length contraction that the entire universe becomes completely flat. So, if, hypothetically speaking, you could instantaneously go at the speed of light and stop instantaneously, with no negative repercussions, as well as control where you end up once the universe expands, would you, in essence, have performed instantaneous teleportation to anywhere in the universe, or at least anywhere along a single direction, from your own point of view? If so, if you were to go FTL, would you experience yourself getting younger, since your personal time is going backwards? Also, would you be going through negative space or inverted space, and if so, what would either of those things be like and/or look like?
Why don’t you want to talk about the episode of Star Trek where they travel faster than light and later turn into lizards because of backwards causality?? 🤣
That's a very good video, I never really looked that much into the math of Tachyons, so it's nice to see someone actually talk about it clearly and in detail.
Now I'm REALLY curious about forward-time tachyons. Wouldn't it make some weird effects going over the speed of causality but still moving into the future? Would this, perhaps, give the sensation of someone distant to be "travelling in time"...? Not completely sure, tho. Also I love your videos so much!
The weird thing is that, whether or not a tachyon is going forward or backward in time _depends on the relative motion of the observer._ Tachyons break physics far too much to be real.
great vid! Keep up the good work. As a nerd who finds it easier to overcomplicate than to oversimplify, i know how tedious translating back down into more common vernacular, AND also retaining the fullness of the meaning and implications of what you are trying to say is an all-but-impossible, sucess improbable, mentally-tiring, frustratingly-tedious, emotionally-exhausting process, no all at once, not all the time, but most definitel all of them some of the time. And i must say, while ive seen varrying degrees of succes at that venture from different teachers in my life and sci-tubers on this platform, i really do believe that somehow, somewhere along the way, you noticed or discovered something in relation to redcing down your data into digestable chunks that are easy to follow, quick to comprehend, and memorable enough to retain. something 'clicked' for you in your understanding in that area to the point were your mastery of it makes most other attempts at it, even amogst youtubes more rcognizeable and more elite content creators, look like poorly practiced recently learned half uninterested attempts. i know its not as simple as what im about to say. having had my own fair share of 'click' moments where something in my understanding of a subject snaps into place suddenly and changes everthing about your perception, as well as having attempted to explain said eureka moment to others only to realize that no matter how i simplified, reorganized or prented the information, there was just some aspect or other of the porocess that i either cant explain properly or they cant grasp properly. But i wish you COULD just explain your secret or method or eureka mont that allows you to be so ghreat at how you do things. But alas, i will settle for watching and enjoying the final product of your superior presentation skill. lol. P.S. Just as an example of what i mean by those little click moment that change your perspective and are really really simple but almost impossible to explain to someone else, heres something for you all to debate and ponder. Did you guys realize you can choose what emotion you are feeking and or vice versa choose not to feel a negative emotion you dont want to feel? And i dont mean the whole, im sad so ill watcha comedy and feel better or something. and im not talking about the clinical psychology way slowly replacing the emotion by identifying triggers and causes and developing coping m,echanisms while using thought replacement techniques to change how you are thinking which in turn directly affects how you feel at any given moment. No i mean like at any given second of any given day in any situation you can .... just .. well.. choose what emotion you want to feel or dont want to feel. just by choosing to. like you dont HAVE to be angry or depressed or sad or bitter. you domnt HAVE to be a prioner to your negative emotion, Your sentient conscious working mind is powerful enough to do that, in an instant, just because you want to. And im not talking no metaphysicaol mystical siritual stuff either... i do this all the time when like i get cut off in traffic and start getting frustrated or when someone is rude or disrespectful to me, or when i recognize some sort of flaw in my thought process. and i really dont know how to explain mto people who dont already undertand, theres no prepping, no delay, no minimum ir maximun time im forced or stuck in an emotional state, If i find myself in an emotional state i dislike or if i desire to be in a different emotiuonal state for whatever reason, i .. just,,, choose to, and i am, And i can see how say, someone with a severe anger problem might be like, yeah, right, there no way its that simple, that right in the middle of seething blinding rage, where you wanna rip someone literally limb from limb while they are alive because you are so mad you wanna hear their screams as they watch the rivers of blood flow from their severed arteries and feel the tendons and joints shredding apart as the nerve fibers and muscle fibers tear and separate as the flesh reaches its maximum elasticy and finally gives way to the force of your unrelenting rage, and just choose, just like that, as easy as simply deciding to, you can become non angry, and even amiable, justy because you want to, and it then just is that way, you just suddenly feel whatever you want to and not the anger if you dont want to, and there no breathing technique, no diary analysis, no funky hippe chemicals involved, no weird witchcraftr rituals or cultic chanting, no psychological processing and no pychiatric alchemy. uyou just choose in you head with words and bam you just are something else? yeah, thats what im saying, And those that have discovered this simple ability, mechanism, whatever you wanna call it, cause ive met others that also can just choose how they feel, its not really all THAAAAT uncommon, can vouch for what im saying here. that it really is just as simple as making a choice to feel or not feel a certain way. But anyone out there who has NOT discovered how to do this, wil swear up and down that theres no way what im saying can be accurate, that you cant just be like, "i choose not to be angry. I choose to be content, i choose to be happy, i choose to be amiable" and you just instantly arent angry anymore and are just whatever you chose. but yes. yes it really is possible, really is that simpole and i use it on an almost daily basis, im not saying you are gonna feel like you won a million bucks, negative emotions do have negative physical effect due to hormonal release associated with them, and unless its another one of thoise click eureka moments ive never heard of as far as i know you cant for example, think a knife wound closed. or think an amputated limb into not being amputated anymore. So the physical side efects of that negative emotion will linger and you might feel that. Nor does it make logical sense to become the same level of excited or happy as say you might be when going to see a concert where your favorite artist is performing, as going from im going to kill you to ha ha im so excited can you believe it eeeeeeeee YYYAYAYYAYAYY! would not only make you look totally crazy and also be totally out of place in a situation that was at serious enough and escalated enough for you to be in an im going to kill you mood. but it would 100 percent be beneficial to you and all others involved if yoiu could say go from im gonna kill you to Im not mad at you anymore and we are able to respectfully and rationally discuss what the issue was and hopefully come tio a resolution that acoomadates all parties involved. so yah, ponder that guys, :P
Nice episode. It always bugs me when people just arbitrary extrapolate the math transformations to get to those backward in time conclusions, so it is really refreshing to see a proper tackle at the topic.
Thank you, and this was awesome, despite making me sad about tachyon and crushing (only some) of my hopes and dreams regarding FTL and time travel. Really well explained and enjoyable!
"Math always gives us an answer, even when our question isn't about reality." Not unlike the Janeway quote: "That's the problem with 'Logic', you can use it to justify anything."
Time wouldn't go backwards for tachyons as it moves past light speed, it would simply be paused just like a photon as it wouldn't be moving through time at all, but would be moving through the universe in a completely different way. Rather than spacetime being compressed into a moment that is as far in the future as it is distant in space like a photon, a tachyon would be moving through space, but not through time at all (not spacetime, just time) in a similar way that inertial mass moves through time but not space. A tachyon's "speed" is just c through space, so it wouldn't have any imaginary numbers in it's momentum. From it's perspective it could move backwards and forwards in time (just as we movie forward and backward in space), however all of it's movement in time (in any direction) would be a single moment of time from our perspective. Therefore, it wouldn't violate causality from our perspective. There would have to be an extraordinary revolution in science for us to ever observe tachyons, even if they do exist, but their discovery would change the world.
This is still my favorite science channel. One of the very few channels I don't just listen to, running in the background, but wanna direct all my attention to (Which sadly means I can't watch right away usually 😅)
Glad you enjoyed it! This is the kind of stuff I want to make and it felt fantastic not worrying about how it would perform 👍. Is it ranking 10th in the last 10 videos? 1st? 7th? I don't know. I didn't check! 😃
The 1980 sci-fi novel "Thrice Upon a Time" by James P. Hogan is all about this. Another take on it is the 2020 Japanese film "Beyond the Infinite Two Minutes". Both are well done and anyone fascinated by the possibilities of such a concept should check them out.
i hate to point it out, but lux is not actually Greek, it's Latin. The greek word for light is "phos" and gave us "the photon". The other two were correct tho :) Also : keep up the good work, awesome videos man!
I miss the background musics from your newer videos. They're as informative as the older ones and have the same humour, but the vibes are not the same.
@1:02 Actually 🤓, 'lux' is Latin; the Greek version would be 'photos' - as in, like, photons. So yeah - scientists do love their Greek and their Latin - till of course, quarks and gluons...
Great video as always. 🙂 Two quick comments: 7:43 "According to Past Me, the signal's velocity is negative so it never arrives". Wouldn't it actually be more like, from Past Me's reference frame, he detects that the signal was mysteriously sent from him to somewhere in his future light cone travelling toward where the satellite would be? In other words from the satellite's perspective, the signal goes from the satellite outward, and from Past Me's perspective the signal goes from his perspective outward. Also it wasn't quite mentioned in the video, but (ignoring all the other issues with tachyons) causality wouldn't be broken by a consistent causal loop, as in Event A triggers Event B triggers Event C triggers the original Event A. Provided it's impossible to break such loops that might occur you wouldn't have a causality paradox. ("But when does the loop start or form? Really they'd simply be "there", they'd always have existed as much as anything else in space-time always existed from that perspective.)
*"Wouldn't it actually be more like, from Past Me's reference frame, he detects that the signal was mysteriously sent from him to somewhere in his future light cone traveling toward where the satellite would be?"* Yes, that's exactly correct. Sorry I didn't make that clear in the video. I should have gone back to the graph and shown it. *"Causality wouldn't be broken by a consistent causal loop."* That's true only if Event A triggers Event B, but that's not what happened in this example. Event B was originally independent of Event A.
@@ScienceAsylum Event B isn't necessarily independent of Event A if you assume all events in space time "already exist". In other words it's a chicken-or-egg question, with the answer in this scenario being neither one happened "first", they both simply existed simultaneously.
@@Bodyknock *"...if you assume all events in space time 'already exist'."* That's the block universe interpretation of relativity, which I don't subscribe to.
@@ScienceAsylum Right, I’m not saying the Block universe model is right or wrong, I’m just saying if it’s included as a possibility then it is a way around the paradox of causal loops. (P.S. If you ever do a video on the pros and cons of the Block Universe model it could be interesting!)
7:30 I don't think this is correct. I have seen calculations that allow causality violation in special relativity if you allow faster than light communication: If A is you and PA is your past you. You can send an infinity fast signal to far away B. For a very fast space ship in the past of PA moving in the right direction, because of relativity of simultaneity, B happens much earlier than A, even earlier than PA. So this space ship can take the signal from B and sends it with infinite speed (or less) to PA.
I once played around with a version of the linear momentum formula to show that faster than light travel with living beings requires making use of imaginary dimensions. That was how I interpreted "jumping to hyperspace" in Star Wars.
Time does not slow down for the electron or the traveller. The clocks are slower against the time coordinate (y axis) but they "experience" their time the same. In the twin paradox neither twin experiences a different feeling. Only when they meet again they notice their age difference.
I love watching your videos, and I’m pretty good at keeping up with most of what you say… but this is WAY up above my head. Theoretical physics just doesn’t compute. Still, thank you for sharing. BTW, FTL was a GREAT game! 😊
0:56 Oops! Apparently, "Lux" is Latin not Greek. I'm not sure how I messed that up. Kind of ruins the whole bit I was going for. Oh well 🤦♂
Greek, Latin... it's all Greek to me 🤣
well, the word 'lux' is related to the Greek word 'leukos', which is usually translated as "white", but also covers the meaning of "bright," or "light" as in "a light colour"; so, it's not totally off 🙂
Maybe they used Latin for Lux as the exception because Tachyons are not real, just like Latin being a dead language.
Im sure we would have a fun chat! Haha
so how fast is infinite speed the pink line needed to travel back in time, just before it becomes infinite?
also what does it mean moving faster than light but still travelling forwards in time,the space between the yellow line and pink infinity speed?
And the bartender said “Hey, we don’t serve faster-than-light particles in here.”
One day, a tachyon walks into a bar...
This game show is actually a metaphor for tachyons.
What is Jeopardy?
This comment is actually funny
The Tachyon then says, "Why not? You did tomorrow."
Hilarious, but isn't the bartender the one moving too fast?
Ha. Ha. Haha. Ah Hah. Hah........ha.
"Math always gives us an answer, even if our question isn't about reality." -- Nick Lucid
May be one of the best math/physics quotes I've heard in a while. I don't know if he was quoting someone else, though.
I wrote that myself. Thanks 🙂
@ScienceAsylum (Tips hat) Don't thank me. Any chance of getting it on a shirt or a mug or something?
Mathematics is not a science - it tells us nothing.
@@ScienceAsylum The way I always think about it is that math is a model. No numbers are "real", just useful to describe stuff, which makes irrational numbers, imaginary ones, quaternions, etc. just as real. Sometimes that does make me wonder if some mathematical equations we use as models are just extremely precise rather than exact. You probably know more about that than I do though.
@@ScienceAsylum correction, it was the quote clone 😊
A fact that is generally overlooked about "time move slower the faster you go", its thats only true relative to another frame of reference. The electron in question will always perceive its time passisng normally, a second will always last a second for it, but it will expercience the outside world to move way faster and distances shirinking
It's like trying to get ready to go out somewhere when one has ADHD, time goes faster than I thought it would once I try to have a shower and get dried then dressed before I leave.
An observer moving at large fractions of the speed of light will observe their own time passing as normal, will observe the rest of the universe as moving slower in time, and having been length contracted in the direction of motion. Because from the perspective of the observer that's moving, it's everything else that's moving.
@@MarcusM-bw9nuYou should watch again and take the above comment in mind. Then you'll probably grasp what happens the right way.
As an example of such relativistic phenomena, let's see what happens to a cosmic ray hitting our atmosphere. The atmosphere is about 100 Km. thick. When struck by a cosmic ray (a particle from outer space at a speed close to that of light), it disintegrates in a cascade of particles that also disintegrate spontaneously or on further collisions in the upper atmosphere. One of the products of such disintegration is muons. Muons have a short life, only some microseconds, so that they can only travel a few kilometres before spontaneously disintegrating. But they reach the surface! For muons from cosmic rays, our atmosphere is not 100 but about 10 Km. thick, and it rushes past the muon at a speed much higher than that of the cosmic ray due to time dilation. So, the muon has time enough to reach the surface: its clock is slowed, as 'seen' by us. For the muon, less than the allowed lifetime is required to traverse the whole of our atmosphere's thickness.
@plSzq1yes, seen from other frames, itself it will experience time passing normally at one second per second and it's usual half time.
Electrons have perception?
That phone call at 0:30 and 7:15 is Christopher Nolan's level genius.
I forgot about the early call. thanks for mention it lol
@@v44n7Call your early self to inform them!
@@localverse 😂
Thanks for the timestamps
Nolan would've drowned out the discussion with blaring noise that he calls a soundtrack
"Math always gives us an answer, even if our question isn't about reality." 🔥
Thanks! I'm really proud of that closing line.
You're awesome!
Isn't that the very definition of insanity?
It's common to use the Special Relativistic equation in hyperbolic form:
c²t² - x² = c²τ²
But it makes more sense to subtract the negative term from both sides to express it in Pythagorean form:
c²t² = c²τ² + x²
Divide both sides by t² to get
c² = c²τ²/t² + x²/t²
That's more relevant when discussing "speed" through 4-dimensional spacetime, because τ/t is the traveler's _rate of aging_ from the perspective of a stationary observer and x/t is the traveler's _speed through 3-dimensional space_ from the perspective of the stationary observer. From those two terms, one can deduce the traveler's speed through 4-dimensional Minkowski spacetime, from the perspective of the stationary observer.
The c² coefficient in the c²τ²/t² term is the conversion factor between the units of time & length, for the two "speeds" (rate of aging and speed through 3-d space). Since units are arbitrary, they could be chosen so that c=1:
c² = τ²/t² + x²/t²
It's a Pythagorean equation, where the square of a right triangle's hypotenuse equals the sum of the squares of the triangle's other two sides. In this case, the hypotenuse is the speed of the traveler through 4-dimensional Minkowski spacetime. (Minkowski spacetime has its time dimension orthogonal to each spatial dimension, which means the triangle is a right triangle.) So the square root of the left side is the traveler's speed through Minkowski spacetime, and it equals c, the same as the speed of light through 3-dimensional space. (And it equals 1 in the appropriate units of time & length.) The equation works for any kind of traveler, including light, and it presumably also works for tachyons. Everything travels at speed c through Minkowski spacetime.
The equation tells us the rate of aging of a tachyon is imaginary, the square root of a negative number. But it's unclear whether aging at an imaginary rate has a physical meaning, so it might be impossible for tachyons to exist.
On paper, them tachyons come from the opposite diagonal quadrant of the Cartesian coordinates you are using, let's put speed on x and energy on y only. Well.. Massive particles will go up to less than c, normal ones. More energy, more speed but never c.
Tachyons are the opposite. 🤔 so with our known observed reference, they are coming from infinite, lowering their energy to reach c but they can't, anyways, they can't get past c, but from the other side 🤔
How is that supposed to happen in the real world as we know it, we can't get past c from one side, tachyons can't from the other... 🤔 😞
@@misterlau5246 : I don't understand why you ask how tachyons' speed through 3-dimensional space can slow down to c. No one is saying it can.
Because their 3-d speed is always greater than c, the equation implies their rate of aging can't change from imaginary to real. And regardless of 3-d speed, the equation says everything's 4-d speed is c.
You are a good science communicator. Many people do not make the distinction between maths and reality, although maths can give the best description of what is happening or will happen, the parameters need to be correct and precise, which a lot of people fail to see.
Hello. Such a good episode Nick. This reminded me of your earlier works, the joy, the fun and the choice of topic. Thumbs up all the way.
Thanks! This is how I plan to handle all my videos there year: enjoy them.
"Fast, fast!" was the first thing that I thought as I read the title of the video
Same!!
Since we're talking about things potentially violating causality, shouldn't it be "!tsaf, tsaF"?
@@petersage5157 😂😂😂
"Gotta go fast!"
"Bradyons" sounds like an honorific awarded to Numberphile fans 😂
I *had* to check this wasn't one of his channels.
I was thinking of the _Objectivity_ and _Periodic Videos_ YT channels.
they are characterized by their Brady number
In the medical field, there is a specialty of medicine and of doctors called Cardiology.
In that sub-field of the medical field, there is a term "bradycardia".
Scientists and doctors love Greek words.
@@zeryphex They sure do. "emia" = presence in blood 😉
Superb, The Science Asylum, Keep It Up. 🌟 Yaaaayyy!!!! 🤗 And I’m Sultan Al-Khaldi
I haven't seen other YT science channels tackle this specific subject despite tachyons being mentioned often. THANKS!
You're welcome. Took me _years_ to finally make this video.
@@ScienceAsylum You could have gotten a jump on things by transmitting it to past you.
@@ddichny 😆
I was able to follow this to the end, but not to my satisfaction as my math brain is too limited. But this is the first time I've heard this subject covered comprehensively. It's a great service you're providing.
Please keep doing the subjects YOU like!
Thank you. Since college (40 yrs back) I pondered what happens if you could go slower than STOP! My intuitive idea was backward time travel… Nick’s closing point is key to many maths revelations. Just because some idea can squeeze an equation out of a maths anomaly doesn’t mean it exists in our reality. Mathematicians generate some incredible meta concepts, but it takes a physicist to keep them grounded……Another brain stretcher was what would we see if Pi was a different value than 3.14…. It took me years to understand that one (ans: it warps things into an extra dimension. In curved spacetime for example pi is a bit bigger making you take longer to approach a mass than the geometric distance would seem…in this case that extra dimension is time. Pi is only the well known of irrational number on a flat surface…space time is not flat, even near Earth.
"Imaginary" numbers do show up in real world engineering, too.
Indeed. I was a bit disappointed at the video’s conclusion, as “real” and “imaginary” numbers are just names that in the context of complex numbers do not mean what they ordinarily mean.
@@germansnowman Of course, that being said; even before the concept of complex numbers was invented, there was "math" applied to mysticism.
"How many angels can dance on the head of a pin?" Etc....
The current conversation about applying "math" to tachyons is not dissimilar: Take something that has never actually been observed, assign a "value" to it, and plug that into an equation which really doesn't apply to the theoretical situation.
But they all must disappear (cancel out) before you can come up with an actual real world answer to any real world question. They do not exist in reality, only as a mathematical tool - an interim placeholder essentially.
@@germansnowman I think that was a pun. In case your username fits, "What I'm trying to say" is an English expression that means that what follows is related only loosely, by metaphor or example, but not literally. He was saying "Tachyons aren't literally imaginary (meaning #1), but they're imaginary (meaning #2)"
@@chuckoneill2023 I get your point. It’s just unfortunate that the common misconception about imaginary numbers being something “less than” real numbers was perpetuated by this otherwise great video.
I really appreciate you taking the initiative and handling all my grumpy commentary and critiques for me during the video. A gentleman and a scholar.
I wish you would do a video on why we cannot use entangled particles to send messages faster than light. In UA-cam comments people often think we can. It would be great to be able to point them to your video. Now I have to explain to them that when we observe an entangled particle it takes on a random value, so we are just "sending" noise to the other particle. And even if we could send a signal, first you have to send many particles to a recipient at best at the speed of light.
A couple of times commenters have been confused about Hawking radiation and I've been able to simply tell them to watch Science Asylum's video on Hawking radiation.
I love the deep dive into how FTL communication with tachyons could work. Math might not always describe reality, but it's always great for the imagination!
I believe this is one of your better videos. I haven't seen another Scituber cover anything quite like this, and you made it easily understood.
Thanks! Glad you liked it. I'm trying something a little different this year. This video is representative of that.
This might be the craziest episode yet! Thank you Nick!
Trust Nick to make 'crazy' seem usual. 😆
I had a couple of good chuckles this time yeah.
I love the channel, makes some pretty high end stuff accessible and entertaining.
I like dabbling in the field, but so much reference material dives into the math. I like that you outline the proof, then get into the "so this is what it means". It's a rare talent.
One of my favourite expressions about theorists is: "They could calculate the square root of a jam jar, but still not know how to open it."
You sir, fly way above that,
That was a very quick 10 minutes. Excellent work.
Thanks!
You always make the most interesting science videos.
Thanks!
props for that Voyager comment .... was a good episode regardless.
Honestly, it was one of Robert Duncan McNeill's best performances on the show and the practical effects were amazing. It was just a terrible premise and it broke continuity. The _writing_ was the problem. I feel bad for everyone else who worked so hard on it.
I wonder what happened to the offspring?
@@ScienceAsylumI think they went with the idea of having a person's physical body existing at all points (at least along the line of travel)* at a given instant in time, doing wibbly wobbly timey wimey things to the subject's biology.
Having observed the consequences they decided trying to recreate this with the whole ship was a bad idea (if it wasn't already).
* They suggested that the ship could exist at every point in the universe at that instant, but glossed over that the ship's velocity was in a preferred direction so at any speed, be it infinite or plaid, it should still not reach points off to the side of the path travelled.
@@ScienceAsylum Still better than "Tuvix"
@@ScienceAsylumI still have a problem with that episode
Kiitos!
Thanks, I’ve got all the info I need to build a time machine. See you last week.
Teşekkürler.
been watching your videos for a long time now and this ones another favorite. always love when the space time diagram comes out :)
4:43. Yes, please don't talk about the salamander children of Captain Janeway and Lieutenant Paris.
Thanks!
Thank you!
I can play this video x10 times.....and still be as confused as my earlier self.
Thanks for the cool stuff and Sweet Thumbnail.
Thanks Nick - awesome explanations as usual. And it's good to come back to reality once in a while 😄On top of that, I think I will add "They're trapped in FTL" to my daily vocabulary! 😀
Tacky-ons are particles that make everything IKEA products
😂🤦
Woah careful with that joke, it's an antique!
They can cause spacetime to spread out, but only near the ankles. That's where bellbottoms came from.
Tackyons are emitted by glue as it dries.
Include Lidl and Aldi
Nic, after your last short video we very glad here in South Africa you've released another amazing video.
I haven't released a UA-cam Short in a while. Didn't really enjoy making them and they were taking brain power away from my longer videos.
At last someone agrees with me 🤟😝🤟Having too many imaginary friends is not crazy 🤟😝🤟
Thanks
Holy moly! Thank you!
"We're not gonna talk about that episode anymore."
Good call.
Honestly, it was one of Robert Duncan McNeill's best performances on the show and the practical effects were amazing. It was just a terrible premise and it broke continuity. The _writing_ was the problem. I feel bad for everyone else who worked so hard on it.
@@ScienceAsylumYeah, that's the thing with Star Trek. You can have amazing sci-fi sometimes, and then switch to very goofy and stupid at the drop of a hat. Sometimes within the same episode. It's good on the whole, but there are some very weird missteps.
I have a big multilayer question for you. In your "what if you were made of light" video, you said that photons experience 0 time, as well as so much length contraction that the entire universe becomes completely flat. So, if, hypothetically speaking, you could instantaneously go at the speed of light and stop instantaneously, with no negative repercussions, as well as control where you end up once the universe expands, would you, in essence, have performed instantaneous teleportation to anywhere in the universe, or at least anywhere along a single direction, from your own point of view? If so, if you were to go FTL, would you experience yourself getting younger, since your personal time is going backwards? Also, would you be going through negative space or inverted space, and if so, what would either of those things be like and/or look like?
Thumbs up for something completely unrelated to the topic... but it was part of the video nonetheless...
The Ninja Turtles shirt ❤🙂🐢 🍕
Loving your content. Willing to think the unthinkable, and debunk so many sci-fi tropes. :)
"How do you say 'causality' with feeling?" 😂😂😂😂
Reminiscent of your earlier videos. This was a great watch & I love the more obscure science stuff that you cover best.
I was hoping people would think that. (The knowledge of the earlier videos but with my current quality.)
Why don’t you want to talk about the episode of Star Trek where they travel faster than light and later turn into lizards because of backwards causality?? 🤣
That's a very good video, I never really looked that much into the math of Tachyons, so it's nice to see someone actually talk about it clearly and in detail.
Now I'm REALLY curious about forward-time tachyons. Wouldn't it make some weird effects going over the speed of causality but still moving into the future? Would this, perhaps, give the sensation of someone distant to be "travelling in time"...? Not completely sure, tho.
Also I love your videos so much!
I believe he's done videos about FTL in the past that may answer some of those questions!
The weird thing is that, whether or not a tachyon is going forward or backward in time _depends on the relative motion of the observer._ Tachyons break physics far too much to be real.
The flaw with phones from the future is a constant busy signal from people trying to reach their brokers.
I drop everything and watch your videos when I get a notification.
What if you were holding a baby?
What if you got the event before the notification?
@@robbirose7032 A small price to pay.
Drop it faster than light
great vid! Keep up the good work. As a nerd who finds it easier to overcomplicate than to oversimplify, i know how tedious translating back down into more common vernacular, AND also retaining the fullness of the meaning and implications of what you are trying to say is an all-but-impossible, sucess improbable, mentally-tiring, frustratingly-tedious, emotionally-exhausting process, no all at once, not all the time, but most definitel all of them some of the time. And i must say, while ive seen varrying degrees of succes at that venture from different teachers in my life and sci-tubers on this platform, i really do believe that somehow, somewhere along the way, you noticed or discovered something in relation to redcing down your data into digestable chunks that are easy to follow, quick to comprehend, and memorable enough to retain. something 'clicked' for you in your understanding in that area to the point were your mastery of it makes most other attempts at it, even amogst youtubes more rcognizeable and more elite content creators, look like poorly practiced recently learned half uninterested attempts. i know its not as simple as what im about to say. having had my own fair share of 'click' moments where something in my understanding of a subject snaps into place suddenly and changes everthing about your perception, as well as having attempted to explain said eureka moment to others only to realize that no matter how i simplified, reorganized or prented the information, there was just some aspect or other of the porocess that i either cant explain properly or they cant grasp properly. But i wish you COULD just explain your secret or method or eureka mont that allows you to be so ghreat at how you do things.
But alas, i will settle for watching and enjoying the final product of your superior presentation skill. lol.
P.S. Just as an example of what i mean by those little click moment that change your perspective and are really really simple but almost impossible to explain to someone else, heres something for you all to debate and ponder. Did you guys realize you can choose what emotion you are feeking and or vice versa choose not to feel a negative emotion you dont want to feel? And i dont mean the whole, im sad so ill watcha comedy and feel better or something. and im not talking about the clinical psychology way slowly replacing the emotion by identifying triggers and causes and developing coping m,echanisms while using thought replacement techniques to change how you are thinking which in turn directly affects how you feel at any given moment.
No i mean like at any given second of any given day in any situation you can .... just .. well.. choose what emotion you want to feel or dont want to feel. just by choosing to. like you dont HAVE to be angry or depressed or sad or bitter. you domnt HAVE to be a prioner to your negative emotion, Your sentient conscious working mind is powerful enough to do that, in an instant, just because you want to. And im not talking no metaphysicaol mystical siritual stuff either... i do this all the time when like i get cut off in traffic and start getting frustrated or when someone is rude or disrespectful to me, or when i recognize some sort of flaw in my thought process. and i really dont know how to explain mto people who dont already undertand, theres no prepping, no delay, no minimum ir maximun time im forced or stuck in an emotional state, If i find myself in an emotional state i dislike or if i desire to be in a different emotiuonal state for whatever reason, i .. just,,, choose to, and i am,
And i can see how say, someone with a severe anger problem might be like, yeah, right, there no way its that simple, that right in the middle of seething blinding rage, where you wanna rip someone literally limb from limb while they are alive because you are so mad you wanna hear their screams as they watch the rivers of blood flow from their severed arteries and feel the tendons and joints shredding apart as the nerve fibers and muscle fibers tear and separate as the flesh reaches its maximum elasticy and finally gives way to the force of your unrelenting rage, and just choose, just like that, as easy as simply deciding to, you can become non angry, and even amiable, justy because you want to, and it then just is that way, you just suddenly feel whatever you want to and not the anger if you dont want to, and there no breathing technique, no diary analysis, no funky hippe chemicals involved, no weird witchcraftr rituals or cultic chanting, no psychological processing and no pychiatric alchemy. uyou just choose in you head with words and bam you just are something else? yeah, thats what im saying,
And those that have discovered this simple ability, mechanism, whatever you wanna call it, cause ive met others that also can just choose how they feel, its not really all THAAAAT uncommon, can vouch for what im saying here. that it really is just as simple as making a choice to feel or not feel a certain way. But anyone out there who has NOT discovered how to do this, wil swear up and down that theres no way what im saying can be accurate, that you cant just be like, "i choose not to be angry. I choose to be content, i choose to be happy, i choose to be amiable" and you just instantly arent angry anymore and are just whatever you chose. but yes. yes it really is possible, really is that simpole and i use it on an almost daily basis,
im not saying you are gonna feel like you won a million bucks, negative emotions do have negative physical effect due to hormonal release associated with them, and unless its another one of thoise click eureka moments ive never heard of as far as i know you cant for example, think a knife wound closed. or think an amputated limb into not being amputated anymore. So the physical side efects of that negative emotion will linger and you might feel that. Nor does it make logical sense to become the same level of excited or happy as say you might be when going to see a concert where your favorite artist is performing, as going from im going to kill you to ha ha im so excited can you believe it eeeeeeeee YYYAYAYYAYAYY! would not only make you look totally crazy and also be totally out of place in a situation that was at serious enough and escalated enough for you to be in an im going to kill you mood. but it would 100 percent be beneficial to you and all others involved if yoiu could say go from im gonna kill you to Im not mad at you anymore and we are able to respectfully and rationally discuss what the issue was and hopefully come tio a resolution that acoomadates all parties involved.
so yah, ponder that guys, :P
Nice episode. It always bugs me when people just arbitrary extrapolate the math transformations to get to those backward in time conclusions, so it is really refreshing to see a proper tackle at the topic.
or 'to see a proper tachyon at the topic' 😀
Thank you, and this was awesome, despite making me sad about tachyon and crushing (only some) of my hopes and dreams regarding FTL and time travel. Really well explained and enjoyable!
"Math always gives us an answer, even when our question isn't about reality."
Not unlike the Janeway quote:
"That's the problem with 'Logic', you can use it to justify anything."
I always like how visually useful you show the time-space diagrams.
It is not accidental though
My ADHD thanks you for the interspersed keyboard clone critiquing you lmfao
I have only watched 2 episodes of your channel, but congratulations on tackling this most interesting topic.
I love your channel so much! ❤ I forget I am learning as I watch.
And remember, it's okay to be a little entertained! 😂
You make everything seem so simple!
This is an excellent layman's explanation of why FTL, time travel, etc. aren't possible in our universe. Great work!
Another very lucid video! Thanks, Nick! 🎉😊
Another excellent video, no problem regarding languages we don't have a classical type of education. Thank you!
"Math always gives us an answer to our question, even when our question isn't about reality" well put man, well put.
Time wouldn't go backwards for tachyons as it moves past light speed, it would simply be paused just like a photon as it wouldn't be moving through time at all, but would be moving through the universe in a completely different way. Rather than spacetime being compressed into a moment that is as far in the future as it is distant in space like a photon, a tachyon would be moving through space, but not through time at all (not spacetime, just time) in a similar way that inertial mass moves through time but not space.
A tachyon's "speed" is just c through space, so it wouldn't have any imaginary numbers in it's momentum. From it's perspective it could move backwards and forwards in time (just as we movie forward and backward in space), however all of it's movement in time (in any direction) would be a single moment of time from our perspective. Therefore, it wouldn't violate causality from our perspective.
There would have to be an extraordinary revolution in science for us to ever observe tachyons, even if they do exist, but their discovery would change the world.
a random thank-you!
Thanks!
Your final point directly mirrored a statement I made to a student today. Fantastic video
I'm surprised you don't have a few million subscribers. You don't even have ONE million. You are so under-rated it makes me sad.
I actually saw this before it was produced. Thank you, tachyons!
a masterpiece of a video!!
and as always i enjoyed the space time diagrams
Thanks!
This is still my favorite science channel. One of the very few channels I don't just listen to, running in the background, but wanna direct all my attention to
(Which sadly means I can't watch right away usually 😅)
This feels like a new style for you and I love this video
Your English is very clear and perfect to practice my listening thanks
I've been subscribed for some time now.
This is the episode I told past me to subscribe for.
I'm glad past you trusted present you 👍
Crank Prank Time Phone works flawlessly
Thank you Nick. Now I have another video I can point to for FTL conversations.
Thank you for interesting content!
Best wishes from Lithuania!
The voyager reference was great! As a trekkie it made me chuckle.
0:55 As a language nerd: "lux" is Latin for light, not Greek. The Ancient Greek root for light is "phos" or "photos", as in photograph or... photon!
I've pinned a correction 👍. Thanks! 😬
This is indeed, the content I want to see on your channel:)
Glad you enjoyed it! This is the kind of stuff I want to make and it felt fantastic not worrying about how it would perform 👍. Is it ranking 10th in the last 10 videos? 1st? 7th? I don't know. I didn't check! 😃
The time travel telephone would be a great outer limits or twilightzone episode. It's a great idea.
The 1980 sci-fi novel "Thrice Upon a Time" by James P. Hogan is all about this. Another take on it is the 2020 Japanese film "Beyond the Infinite Two Minutes". Both are well done and anyone fascinated by the possibilities of such a concept should check them out.
i hate to point it out, but lux is not actually Greek, it's Latin.
The greek word for light is "phos" and gave us "the photon".
The other two were correct tho :)
Also : keep up the good work, awesome videos man!
I miss the background musics from your newer videos. They're as informative as the older ones and have the same humour, but the vibes are not the same.
@1:02 Actually 🤓, 'lux' is Latin; the Greek version would be 'photos' - as in, like, photons. So yeah - scientists do love their Greek and their Latin - till of course, quarks and gluons...
I've pinned a comment with a correction 👍
Great video as always. 🙂 Two quick comments:
7:43 "According to Past Me, the signal's velocity is negative so it never arrives". Wouldn't it actually be more like, from Past Me's reference frame, he detects that the signal was mysteriously sent from him to somewhere in his future light cone travelling toward where the satellite would be? In other words from the satellite's perspective, the signal goes from the satellite outward, and from Past Me's perspective the signal goes from his perspective outward.
Also it wasn't quite mentioned in the video, but (ignoring all the other issues with tachyons) causality wouldn't be broken by a consistent causal loop, as in Event A triggers Event B triggers Event C triggers the original Event A. Provided it's impossible to break such loops that might occur you wouldn't have a causality paradox. ("But when does the loop start or form? Really they'd simply be "there", they'd always have existed as much as anything else in space-time always existed from that perspective.)
*"Wouldn't it actually be more like, from Past Me's reference frame, he detects that the signal was mysteriously sent from him to somewhere in his future light cone traveling toward where the satellite would be?"*
Yes, that's exactly correct. Sorry I didn't make that clear in the video. I should have gone back to the graph and shown it.
*"Causality wouldn't be broken by a consistent causal loop."*
That's true only if Event A triggers Event B, but that's not what happened in this example. Event B was originally independent of Event A.
@@ScienceAsylum Event B isn't necessarily independent of Event A if you assume all events in space time "already exist". In other words it's a chicken-or-egg question, with the answer in this scenario being neither one happened "first", they both simply existed simultaneously.
@@Bodyknock *"...if you assume all events in space time 'already exist'."*
That's the block universe interpretation of relativity, which I don't subscribe to.
@@ScienceAsylum Right, I’m not saying the Block universe model is right or wrong, I’m just saying if it’s included as a possibility then it is a way around the paradox of causal loops. (P.S. If you ever do a video on the pros and cons of the Block Universe model it could be interesting!)
7:30 I don't think this is correct. I have seen calculations that allow causality violation in special relativity if you allow faster than light communication: If A is you and PA is your past you. You can send an infinity fast signal to far away B. For a very fast space ship in the past of PA moving in the right direction, because of relativity of simultaneity, B happens much earlier than A, even earlier than PA. So this space ship can take the signal from B and sends it with infinite speed (or less) to PA.
Thanks Nick for another great video.
I once played around with a version of the linear momentum formula to show that faster than light travel with living beings requires making use of imaginary dimensions. That was how I interpreted "jumping to hyperspace" in Star Wars.
👍Thank you for another video filled with interesting facts. Time travel is the topic that will always be interesting no matter what.
As usual, Nicely done.
Great video nick! Since you’re in the topic of time travel maybe next video could be about wormholes
0:57 Wouldn't lux be Latin for light, not Greek?
The Greek word is Φως, and my understanding is that when we explain such Greek words using our Latin-derived language then it's going to look Latin.
@@AlleyKatt Apparently, the Greek etymological step for "lux" is "leukos" 🤷♂
A small correction: lux is Latin for light. In Greek it would be phos, like in phosphorus or photon
I've pinned a correction 👍. Thanks!
Thank you for making this
Time does not slow down for the electron or the traveller. The clocks are slower against the time coordinate (y axis) but they "experience" their time the same. In the twin paradox neither twin experiences a different feeling. Only when they meet again they notice their age difference.
Love that you brought up "that" episode of VOY.
Love your graphics Nick thanks
No. "Lux" is _Latin_ for light. The Greek is _phos_ (φως), which is where "photon" comes from.
I really like your videos. They are very interesting.😊
I appreciate the Voyager reference, and the implied feelings contained therein
I love watching your videos, and I’m pretty good at keeping up with most of what you say… but this is WAY up above my head.
Theoretical physics just doesn’t compute.
Still, thank you for sharing.
BTW, FTL was a GREAT game! 😊
Loving this Tachyon wave of videos I've been binging today.
Everyone's playing the algorithm smhw.