Awesome intro to SR. I personally think 'the best way' (if there is a single best way, which as Sean says there probably isn't) to teach SR is to emphasize the analogy between Euclidean rotations along the unit circle and Lorentz 'rotations' along the unit hyperbola. People have a strong intuition for rotations along a circle, which they can use as a nice bridge to the much less intuitive Lorentz transformations, because really it's the same basic idea: make a transformation that preserves a distance. I also like this approach because it makes it easy to do a 'symmetry-forward' intro to the subject, which lets beginners see the power of symmetry in a simpler context that will then become useful as they advance.
This is the one I have been waiting for, space time, a dazzling feat of the human mind, I hope I understand it better, its a difficult topic for a layperson.
To get a better intuition for how spacetime diagrams work in Special Relativity, especially the way the axes shifted and sort of "pinched together" for the person in motion (the technical term for which is "Lorentz Transformation"), I highly recommend Minute Physics' series on it. He had a physical device made that recreates the hyperbolic geometry of those transformations in a very visually compelling way. ua-cam.com/video/1rLWVZVWfdY/v-deo.html
This is at least my fourth attempt to understand spacetime. This is the second video I've watch and I've also read about it at least twice; once was in Carroll's book "From Eternity to Here". I still feel like I only kind of understand it, so maybe I just don't have much of an aptitude for complex physics.
@@alankoslowski9473 Think in this way: the trick here is that c is invariant i.e. c holds the same value regardless of the coordinate system from which c is measured. If you start to move, you will find yourself in a new time coordinate t' and in Newtonian mechanics the x' coordinate will be perpendicular to t' but in that case c will not be invariant. The only way for c to be the same in the two coordinate system is when the x' coordinate has the same angle to c as the t' coordinate. Therefore this skewed apperance of the primed coordinate system, which, in turn, creates time dilitation and length contraction. And yes, I'm more fond of the traditional way of teaching relatively ;-)
LOL! There is a part of me saying,, "He's talking about the closest star to our solar system ya moron!", but there's another part of me saying, "Ha! He's got ya there, Sean!"
I love that this series exists. If only the other people I'm with in lockdown watched it too, I would be able to have conversations with people about topics more interesting than the weather and tiger king.
The durian fruit is also much like strings in string theory. A person gets a stick and bangs on it to hear the vibrating beauty inside like the universe holds. Different vibrating sounds mean different tastes in each durian. They can be hard or soft in different variations. So the decision is not just 2 choices of I hate it or I love it. The people that hate it only smell it. The people who love it feel deep down in their soul. Something AI can never have. I doubt a human made machine, even one reaching the singularity could ever develop a loving nurturing soul. The durian analogy is way more complicated than the people in the podcasts implied, much more. When I see AI can do that I’ll be amazed. Until then it is just a robot. An object forced into slave labor.
These and Brian Greene's Equation of the Day have been a great way to review all the physics I haven't seen since university many years ago. Thanks to all the scientists and mathematicians keeping us sharp with these lessons!
Thanks Prof. Carroll, this lecture was amazing. I am very grateful. While watching, I think I grasped why the doppler effect in radios occur (in ham radio, it happens when you communication with satellites in low orbits). And indeed in the wiki page en.wikipedia.org/wiki/Doppler_effect it says it's related to relativity! WOW! Before it was just a mysterious thing, now it (kinda) makes sense thinking in terms of the CONES in space time, and radio waves moving at the edge of the cone. I will have to think more about it. But if you happen to do a generic Q&A, perhaps you can mention/explain it? THANKS!!!!!!
You're not stupid, you're sane. There's no proof for Minkowski's interpretation of the Lorentz transformations. Lorentz himself said time dilation is a real effect of clocks being slowed down when they move through the vacuum.
Photons and gravitons are not on all fours here in one very important sense. Photons are all around us while gravitons are hypothetical entities imagined to exist as a consequence of some attempts to shoehorn a successful statistical model of the microworld on to the very large-scale properties of extension and mass. It is far from clear the project of seeking a subatomical mediation particle for the force we infer from the nature of the motion through spacetime is well motivated, let alone that the particulate ontology of one of those efforts should be viewed as just another thing in the world, like light. The universe is under no obligation to conform to our theories, no matter how preposterous they may be. Otherwise, keep them coming - the videos, I mean. Thanks much.
There is also another way to see that it isn't about the acceleration: The Fermilab channel on youtube did a video about this topic some (space-)time ago where they introduced a second spaceship flying towards the observer on earth. The two spaceships exchange their times while passing each other (without stopping) and the second spaceship arrives on earth with a shorter time than the observer on earth measured, even though none of the three observers ever accelerated.
You mentioned that people like string theorists often think about extra dimensions of space but still just one dimension of time. I'm curious whether there are any theories with extra time dimensions? Mathematically it seems like it would be easy to add an additional dimension with a negative sign in the metric, but i'm having trouble thinking about what it would do to causality or anything.
Professor Sean Carroll, kindly suggest an updated book for "the biggest ideas of the universe".....theory + math both.....with required math.....Thank you Professor.
Thanks prof Carrol, Finally I better understand some aspects of special relativity which was for me still rather vage and a bit confusing. Many thanks! Allow me to ask a question a bit out of context. If gravity is a pure consequence of the nature and curvation of spacetime and not, as often said “a real force”, why do physicists want to unify gravity with the 3 other forces? Is it correct that gravity just seems to act like a force since the path of an object in a gravitational field undergoes a linear acceleration as a consequence of the shape of spacetime? Thanks a lot.
Thank you so much for these! I just won your new book in a giveaway (thank you Matt Ingebretson!!) and I'm extra excited to have these lectures to keep me thoughtful while waiting for it to arrive.
Question: are there any theories that include multiple dimensions of time? or; is there a useful reason that we might consider multiple dimensions of time? Thanks for the whole series!
not attempting an answer, but offering questions: What if we approach this by (re-)asking "What is measured?" What do we measure, when we measure "time"? Casual / informal / unpolished answer: "change" = the change of seasons, the change of the position of the sun in the sky, the change of growth in our children, the change in decay, etc.pp. What do we measure, when talking about "space"? again casually speaking: the position of any given object as well as the distance to a reference point. What I think "spacetime" beautifully does, is stating something painfully trivial: time and space viewed separately are basically cross section and longitudinal cut through the same cake, and it would be better understood if asking both when and where. In this sense, time and space already are dimensions both explaining the same phenomenon. How would adding more dimensions to "time" help us understand this phenomenon better? or in other words: what could we add to "before" / "now" / "after" that would explain the overall phenomenon better?
You could have a second time dimension in which the two together represent the world as experienced by you (your worldline) and all the other worldlines not experienced by you but which are also possible.
Looks you are only one watching with attention. Twin paradox is not what Sean told us. Just see wikipedia for a start. I devised a solution in SR, just lazy to publish, plus I'm not sure my solution is original.
52:35 "you send out an infinite number of little rocket ships travelling at faster than the speed of light, at infinite speed, of course you couldn't actually do this" - disappointed.
Thanks for a great video. My question is about whether space-time is taken as a physical concept or as a measurement framework. In GR Einstein seems to define space-time as resulting from what one measures with a ruler and a clock; how is it defined in e.g. QFT? In GR it seems that space-time is dependent on the energy-momentum structure in space-time, so it is sort of implicitly solved. Are the fields in space-time the source of space-time? Personally it seems to me more satisfactory to think of space-time as a non-physical framework we use to order our perceptions and measurements, somewhat like a 3d spreadsheet.
Time causes space to expand. Time uses energy from the universe, causing the universe to expand and the moons orbit to become longer, the moons orbit moves farther from the earth. Time is a measure of the entropy of the universe, of space.
Great video very educating! I have a question that if space=V*time, then you said light speed is the limit. But what if something travel faster than light? Will this equation cause more space to be created if speed exceed light speed and does that mean something could reach other space dimension if it travel faster than light? Thank you!
Thanks for this great lesson, but i am still struggling with a question regarding the Twin Paradox: what if space is positively curved and the universe is closed? The one twin starts the journey with the rocketship and is travelling just in a 'straight' line all across the universe. As space is positively curved and closed he would just arrive at where he started his journey. How could it be that only the twin who is travelling is aging more slowly? Arent Both, the twin in the rocketship and the twin staying at earth, in an inertial reference frame? From the persective of each of the twins, the other is in motion and time should tick slower compared to the 'stationary' twin. I am confused
I think the trick here is that you have to undergo an acceleration to experience the time dilation relative to the stationary twin. So since the stationary twin never moves in his own frame of reference he never feels an acceleration. The twin you postulate moving around the closed universe had to undergo an acceleration to make the trip. Hence his time is dialated with respect to the twin who never moved. Even though it looks like the stationary twin moved from the perspective of the twin who made the trip, he really didn't move because he never underwent an acceleration. Whew...... that was a long explanation, but i think I'm correct.
I think you'll find Donald has a beautiful understanding of spacetime; one of the greatest most beautiful understandings of it ever, and he's going to do more to understand it even more beautifully great than anyone ever, by injecting it with beautiful sunlit disinfectant, grabbing its genitals and building a wall around it. Covfefe
I'm not sure whether I feel smarter or dumber after watching these videos. I'd watch them more than once, but I'm afraid I'd figure out which one it was. :)
So, if there is no simultaneity, does this apply to causality too? Specifically, does this in anyway, explain the delayed choice double slit experiment?
@@blackieblack thank you for your response! So paraphrasing what I understood, if we improve the detectors to be more efficient and move the pattern detection screen further by orders of magnitude, can we glean any new knowledge?
I don't understand how this doesn't have like millions views, this is the most interesting thing in the world and mr. Sean is such a great talker, thanks for sharing what goes on in your genius brain 🙏
Sean is a wonder of our world, that expands our perspective, however complicated it may be...awesome work Sean. I've seen a good portion of your online videos, always captivated, as I crave the amazing guidance and understanding you bring to theoretical, and traditional physics.
Sean, you are a nice person but you do not understand the Relativity! On ~18:00 you say Feynman was mistaken to say that Time Dilation caused by acceleration. Feynman was absolutely right! You are mistaken by saying Time Dilation is caused by traveling distance! Just imagine two two clocks, stationary relative to each other, at different heights on the Earth. For the higher one there is more Time Dilation, and it is only because of different accelerations. No traveling distance is involved.
As you move faster through space you move slower through time.(velocity based time dilation) As you move closer to a large mass you also move slower through time. (gravity based time dilation) While it's true you had to accelerate to achieve a faster velocity through space, the effects don't stop once you stop accelerating. Agree?
He was talking about the Twin Paradox. It is possible to set up the experiment where no acceleration is involved (by having an inbound and an outbound traveler) and the twin back on earth will still age more. The difference is the two different reference frames of the travelers versus the one reference frame for the person on earth.
thank you so much please continue with this that course was priceless the top down point of view that you exposed was extremely convenient for me because I needed a tidy framework to organize what I knew and understood about relativity and this is just on point
As someone who grew up with more Buckminster Fuller geometry than Euclidian geometry, your "I'd rather do it this way" approaches are much more accessible to me; I like when you go there. I finally get relativity, since you are willing to move away from the x, y, z coordinates into a language that is more spacetime friendly. Thank you!
Really great videos. Thanks. It would be nice if in your Q&A could talk about the special case of photons and how they "see" the Universe and (not) experience time (also maybe in the context of their interaction with other particles, e.g. in the photo-electric effect, when they "appear/disappear")
Hey Mr Carroll. Multiverse is true because particle small enough to be in a quantum state is an universe in it self. When you use calculus in Feynman diagrams, you connect relativity and quantum mechanics.
Are we always traveling at the speed of light through spacetime no matter what our speed? How you were describing Minkowski space reminded me of this blog post: medium.com/predict/we-all-travel-through-spacetime-at-the-speed-of-light-d60cb389dfc2
How certain are we that the speed of light is invariant throughout the entire history of the universe. Like just after the big bang was the speed of light the same? Is it impossible to know?
I always wonder what it'd be like to be a photon. If length contracts as you approach c, and photons travel at c, then how big would a photon think itself to be from its own frame of reference? Infinitely large? Is that the flip side of considering how a photon experiences zero time for its entire existence? If I were a photon, would I ever even feel like I existed at all?
I would also love it if Star Trek showed the Enterprise shrinking smaller and smaller as it approaches warp. Little teeny tiny toy spaceships zooming past a gigantic hydrogen atom.
Well, the length contraction would only happen along the direction of motion. So assuming it moves in a straight trajectory, it'll only shrink in that one direction and effectively look like a giant pancake at warp speed.
In the space lecture you mentioned possible extra space dimensions on top of the three we experience. Could there be also more than one time dimension?
Not sure about your explanation that it is not the acceleration. In your spacetime diagram, the two observers accelerate for the same amount of time, but that is only in that particular reference frame - the global frame where the twin was mostly at rest. If you looked in the comoving frame of the twin who ages less, I think he will see the times for the accelerations as quite different. One can of course analyze everything from the point of view of the twin who ages less, during the first outbound leg, he will indeed age more (usual special relativity calculation), but when he accelerates, he will observe a gravitational field, and then see the second stay at home twin age more because he is higher up in a gravitational potential - and then during the inertial return trip he will age more than the stay at home twin - combining all the effects leads to the same special relativistic result of the stay at home twin. I think what you say is partially correct, in that it is the large distance separation and thus large effect of being in a higher gravitational potential, that causes the stay at home twin to age more from the perspective of the accelerating twin. Thanks Sean for these great videos.
10:26 Thank you for that information!! When you put it on a grid like that, it becomes clear (rather, it did to me) that if you have and x and y Axis, and two point, the line or path is the slop...but, if time isn't included, then we are just measuring distance (rise over run in units relating to linear space only). When we change our vertical axis to represent time, we know get more useful information. Our slope is still rise/run but now it's: _time(duration)/space(distance)_ instead of *space in one direction (distance)/space that is 90° off in angle of direction (distance)* Now, we can see the time it takes to travel a certain distance of space (using whatever units we choose to use, so long as it's constant: light-years, MPH, whatever). When that spacetime is curved, then using just space to find the shorter path from point A to point B is (as stated) "kind of like" walking up to a valley and deciding that the only way is to walk down, through and up the other side of the valley... when, if you had the ability.... flying across would take less time, even if that meant having to do more work (more events) than if you had just walked. You have to get the plane ready (fueled up, know where you're going to land, do a ton of preflight work), take off, fly that short distance, land and put the plane away. Intuitively, it seems like walking is less work and the easiest way to get from point A to point B..... but, if the time it takes to walk there is longer than it would be to go through the work of flying there, then the reality of the situation is: the shortest path from point A to point B, considering the time each choice (walking vs flying) takes, might be a longer path through space. In other words: walking would take less steps (events) and you would walk fewer miles, but you would take longer, making it the longer of the two routes time wise. If you flew, you would have to go through considerably more steps (events) and your path, including the flight, might be a longer distance of space covered. However, if you covered more space in less time by flying, then flying would be the shorter of the two routes, time wise. It's similar to space in that flying would be a straight line through space, making it the shortest path... but in space, most of the time... flying over a valley isn't an option for us 😂 so, it's kind of like space, like you said, but the shortest path through spacetime might be through more space than time. You get there sooner than just covering a straight line in space, but you end up covering more space...just in less time. Makes way more sense now! Thank you! 👍🤘
Awesome presentation Prof. Carroll. I'm very impressed with these casual videos you are doing. Question: Your last written statement, "General Relativity: Spacetime is dynamical, responding to matter / energy. => Gravity". Since we cannot measure space, time or space-time without physical tools made of matter / energy. Wouldn't it be equally true to say, "Matter is dynamical, responding to other matter /energy nearby => Gravity". The point being, we can't observe empty space-time, we can only observe its effects on the observable matter / energy it contains.
I keep coming back to my highschool physics classes when they talked about the difference between distance and displacement. I know they are different but how significant the difference is is not so intuative
29:00 3 seems like a clumsy number, what would happen to our maths if the speed of light was 1 instead? i have wondered for ages why the circumference of a circle is such a weird number, i joke that it's the registration number of our universe, a different universe would have Pi as a different number, and i wonder, is our universe is bent, could Pi not being a round number be due to "our" circles all being warped? it's okay, i am on drugs. but to get back, 300,000,000 meters per second, would maths and cosmology still work okay if we made it 100,000,000 - surely our numbering intervals are based on the the amount of time it takes to get round the sun, but the actual length is arbitrary?
while i am here, i was watching one of the debates, with the bhuddist (wallace?) and he kept remarking about how we do not understand consciousness, and one thing that has bugged me is the feeling of why am i here now? we talk about what a great era we live in, the music, landing on the moon etc etc, and it got me thinking, why is my consciousness conscious NOW? surely a conciousness could appear in anyone - i could have been born someone else (if you see what i mean) born someWHERE else, but also, why at this time, surely my consciousness could awaken at any point in time?? however, after watching sean's talks it makes me realise this is daydreaming rather than physics, my consciouness can ONLY be here and now, whatever it is that makes me awakw compared to a rock is still just physical, it is not separate from time and space.
I, aka Sean, preferred to start from scratch. If you simply start from scratch and analyze "Motion", and do so properly, you will soon discover SR and all its causes or its foundation, which brings it about. No knowledge of Newtonian physics is required to do this. The less you know about physics, the easier it is to discover SR all by yourself.
I’m not sure our model is correct. There is no evidence that time is scalar, I have never seen anyone or anything be anywhere except the present. Granted the light from their present takes a while to get to my present, but light can only move one Planck length per Planck second, and the Planck are very small if gravity is strong so it can take multiple plancks seconds for me to observe what happpened over there. Neutron decay cosmology is the physical process solution to black hole information paradox and fine tuning.
What about unavoidable conscious computations resulting from the acceleration. We have the motor and sensor homunculi which will always map the input from our sensory stimuli and it has an analog input since our blood is incompressible and has a mass, viscosity and so on. The electric signals will always be directly correlated to the fluid flow and its mass will always respond to a force and thus J/m. Unavoidable energy into/out of our system as a result of the change in distance distance.
let me start by saying I dropped out of high school in 9th grade, at 36 i went back got my ged, and now at 40 im watching this brilliant teacher and actually able to understand some of this lol, good job Mr. Caroll big fan of your many worlds stuff too!
If the galaxies are accelerating away from each other at a faster and faster rate then that means humans live longer now than they did in the past directly because of that?. Or is our galaxy moving on a straight line trajectory with a constant time lapse?, but then the galaxies and universe itself is not accelerating if that's true?. I think I really misunderstand it because it seems that if speed/acceleration effect time and the universe is expanding faster then human avg life span should have a direct correlation to the solar systems accelerating speed through distance even if on a conceptual straight line?. Maybe I am making a very naive maybe childish assumption that our solar system holding us can act as a big spaceship through space-time?.
There is a type of Space-Time diagram in which the scale for both systems is the same. They are called "Loedel Palumbo Diagrams" and with them any analysis of special relativity is significantly simpler. They were developed in the mid-20th century by the Uruguayan physicist Enrique Loedel Palumbo from the simple, but brilliant idea, of considering in a diagram of Minkowski not one, but two "mobile" systems with the same speed, but in opposite directions and then remove the "fixed" system from the middle and... voila! you have two systems with the same scale! .The relative speed between these two systems is now given by the sine of the angle between the axes, not by the tangetic and trigonometry is that of all life. It is a shame that they are not very widespread. This is a link to the demo ua-cam.com/video/o4kKeG8PyyM/v-deo.html
The Chinese use this word '宇宙' (pronounced 'Yu Zhou') to refer to the universe. It's a compound word that can be traced back 2,300 years when the first recorded use was by a philosopher Shi Jiao (c. 390-330 BCE) in his book Shizi. He explained the word as such: the first character 宇 means 'up, down, and the four directions' (上下四方曰宇), while the second character 宙 means 'ancient, past, present and future' (古往今來曰宙). If examined from a modern standpoint, his view of the universe as a whole was exactly the definition of spacetime, because he already combined the concepts of all directions (space) and all tenses (time) into a single notion. These guys must be onto something!
so do people at the equator experience less time than people at the poles? (given that the equator is going ~1000 mph?) do people near the equator die at younger age, since they exhaust all their "biological potential" relatively more quickly than people at the poles?
Electrons, like atoms, and black holes, and the universe as a whole, are horn toroidal fluid vortices (hence "point-particles") in/of the single, scale-uniform 'super-fluid' medium (I call it the SUM, a.k.a. "space-time") whose self-relative motion (a.k.a. "acceleration"; "momentum"; "push") as vortices and waves, comprises the evolving (hence "time") structure of the universe and all of its content "physical objects". Therefore we can say that the "material universe" is 'pure motion' (primarily point-radial in trajectory). The Einsteinian "time dilation/ length contraction" principle applies to the SUM itself, meaning that its self-relative motion ("acceleration" as 'motion relative to itself over time') is the mechanism by which the otherwise absolutely homogenous SUM 'self-differentiates' into the structural diversity of the observable universe, including our own bodies. Also, therefore, not only do massive objects "curve spacetime", massive objects ARE "curved spacetime". The inflow of the SUM equals the point-radial outflow "expansion" of the SUM compression wavefront that is the surface of the mass-object (e.g. the Earth). Ergo the "gravitational (and smaller scale) field(s)". Since SUM fluid vortices, and every complex manifold thereof, including ourselves, constitute 'I/O devices' (inflow/outflow; input/output; positive/negative; "yin/yang"; etc.), we can say that the physical universe is comprised by an otherwise, absolutely continuous SUM "simulating" (by means of its self-differentiating, self-relative motion) a "discrete particle" - based "material universe" as "a universal self-organizing network of distributed I/O devices" which are manifested in terms of their inter-communication by means of the specific sequence of SUM 'vibrational acceleration waves' traveling at the "constant, finite, but asymptotic limit for all mass-objects" speed of light which they emit and absorb. We "human beings" are momentum routers ("pushers" of "things") in that network. In order for there to be a "push", there must be a "something else" to "push against". "Yin/Yang". Consider that every "sensation" - i.e. that you are "conscious" of - is comprised of a "push" (or vibrational series of "pushes") at some scale, at some amplitude, in some 'direction', as a "transfer of momentum"; a displacement of a mass object from its otherwise geodesic path. So the "material universe" is apparently a self-configuring momentum-routing circuit /network. "Consciousness" is 'a self-configuring momentum waveform' in/of the SUM. P.S. "Dark matter" is the SUM itself concentrated around its "material" vortices, and "dark energy" is its larger-scale flow. ua-cam.com/video/MmG2ah5Df4g/v-deo.html 0:22/11:57 They are being carried along by the outwardly expanding flow of the SUM (scale-uniform medium) itself from its horn toroidal fluid vortexual architecture "output". They are not, themselves "accelerating" (undergoing "proper acceleration") by means of an 'on-board' power supply. Thus, in this case, they are not moving "through space over time", they are moving "with space over time". Light waves are the universal 'CPU clock ticks' of 'time'. They make up the 'Cartesian coordinate system' of the 'space-time epic' in which we are taking place. ... Call the Y axis "time", and the X axis "space". Let your eye be at 0 looking in the positive Y direction, and let any other detector be placed anywhere else along the X axis. The photon (or physical increment of "time") is propagating toward your eye, or other detector, as a spread-out 'shock wave' front, and collapsing point radially toward its detector, only being "detected" when the momentum (acceleration) pulse it is transferring through the SUM (scale-uniform medium, or "space-time") literally from its horn toroidal 'point' of origin is transferred to its corresponding destination point of detection. The universe might be described as a 'self-calculating quantum computer'. Let's discuss: ua-cam.com/users/onemediuminmotiondiscussion
Around 10:25: What if point B is directly above A in the spacetime graph? i.e. you don't move at all in space, but only in time? how do you take various paths through time?
Hi Sean and thank you for all your videos (BIU and Mindscape etc), I find your openmidedness to be wonderful and informative. I just watched episode 6 of BIU and I have 2 questions please. 1/ As we understand it, at the start of the big bang, were there massless particles traveling at the speed of light or did we have to wait until photons came into existence? and 2/ Do we know how many light years we are away from the BB and therefore (given the light cone from the BB) how much further past us the cone currently extends? Thank you - Jamie
I'm a little confused. @50m it's written: l^2 = t^2 - x^2 from Pythagoras, it seems it should be: l^2 = t^2 + x^2 or am I missing something? Sean says of l prime "it actually has an extent in time...therefore it is in fact contracted." Which implies it is l^2 = t^2 - x^2, but I don't get it. Maybe it has something the fact that the "shorter" l prime looks longer than l (when it's in fact shorter). Probably an effect of this simplified diagram. Anyone? I guess I can't apply the Pythagorean Theorem, but must instead use the "Minkowskian Theorem". From 22m: elapsed time, (tao, T): T^2 = t^2 - x^2 From 50m: elapsed space, (length, L): L^2 = x^2 - t^2 is this to say elapsed time (squared) is the opposite of elapsed space (squared): T^2 = -L^2 or even T^2 = (Li)^2 I thought I was coming to understand spacetime, but now so many questions....
I sometimes think, since I don't have the math background to even START to 'know' about relativity 'completely', (actually, I guess that means I ALWAYS think that), anyway, not having the math background, I think that by getting as many different versions of the explanations (for the layman) of relativity as I can, that I'll get more of a 'kick' out of the downright cool aspects of the subject. Well then that means I have to say that the two or three minute explanation of "length contraction" given in THIS video is by far the best one I've seen, in that it allowed me to integrate all the other explanations I've heard in a way I just can't adequately describe. It was truly so succinct and clear, in the context of this group of videos, that I feel my understanding has taken a 'quantum leap' after absorbing it. BRAVO! AUTHOR!! AUTHOR!!! :-)
Professor Carrol. Thank you so much for explaing things in a clear manner. I have a question that is naive.. If the energy of × is quantum, is the speed of lights energy up to 10 out of 10 on the quantum scale? As in light has reached the maximum charge? I wonder because how can red and blue light shift occur? No doubt you have covered this subject many times. (Got a link?) I am very interested in your top down approach to teaching. At school learning was difficult as it seemed to have no practical applications.. Maths was extremely tedious, and I think its the teacher not the student that trail blazes your enthusiasm. As a fan boy I have bought your book Something Deeply Hidden and was hooked.🤓
Why is the speed of light the fastest, well, let's say that light is actually moving almost exactly at the speed of time itself, then there-for Light experiences nearly 0 time. So even if it takes 5 minutes of light to reach you, in your perspective, it takes time 0 second, or (0.000000000000000000000000....1) seconds. Then in that case, if you actually travel faster than light, you would need to technically travel backwards in time. You're welcome again physics. But again, it's all theories. You need solid testable proof from tons of readings and observations. Ect. Otherwise it's all fancy sounding guesses, aside from applicable sciences. Also traveling while experiencing 0 time (moving exactly as fast as time moves) would look like a straight line horrizontal on your t / Xy grid. So you see you experience no time because you are moving just as fast as time, so there-for time is not "Passing you" physically, because time is actually a motion itself.... now that'll mess with your mind. If you observe time as a substance that's moving. Gives a whole new meaning to '"space"time'
I tuned in during covid on almost all of your streaming lessons. Later I decided to copy these streaming versions of your biggest ideas to watch again so as to get better notions of the topic. The stream I think are much much better in terms of understanding these difficult physics subjects. (I think the books are for coffee table conversation pieces) The original streaming with the diagrams, the math, the explanations are what got me past the dark muddle and feel I have an even better grasp of these topics. This stream on the time cone when shown with the coordinate explanation really is the turning point for me understanding spacetime. The college level courses in calculus (differentials and integration) which I struggled with also was a huge help when following your streams. But it gets bumpy by the time we get to quantum physics.
On the twin paradox. Let's say the two twins are A and B, or Ann and Bob. Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years. Ann thinks 10 years have passed, and Ann and Bob agree that Bob is two years younger. The confusion arises not because there are two equally valid inertial rest frames, but because there are three. In special relativity there is no acceleration to speak of. The three inertial frames are 1) at-home twin 2) the going-away twin and 3) the coming-back twin. It doesn't make any difference that the last two are physically the same twin. They still define different inertial frames. An important question is what is the relative speed of the two Bob frames? On first glance, it might appear that one is going 3/5c in one direction and 3/5c in the other direction, so that the difference between the two frames is 6/5c but special relativity does not add speeds this way. The actual difference is only 15/17c, fast but not faster than light. Now, since special relativity lets us use either rest frame, we assume Bob is the at-home twin. Ann speeds away at 3/5c. No problem so far. But after 4 years of waiting, Bob must change his inertial frame. If we allow Ann to return, we've only restated the problem with the names switched. In the first version, Ann stayed in an inertial frame, and she must stay in an inertial frame in this version. Bob zooms off after Ann at 15/17 light speed and of course catches up. It takes him 4 years, and he has seen 8 years since Ann left. Ann has aged 10 years. You get the same result, and there's no paradox.
Spacetime-ly we'll circle back to an energy ride, but first let's talk more classically about spacetime and the limit C. why the idea of union counts aside from space and time as separately. it's really about relativity, theories special & general clearly. we'll be presenting top-down Minkowski's 4D (not starting with Newton's universality) then get back to how everyday we see. gone Newton's space and time so absolutely, not just adding a coordinate to three, when we travel from point A to B. a new structure mathematically, paradoxes go away conceptually. how is going A to B in some ways like traveling along in space 3D? a clock's elapse not coordinately, and light cones demonstrate how spacetime plays, all proper time intervals will agree. (but order may not so easily if moving non-inertially) [chorus] spacetime's a dynamic, there's no need to panic, when shifting into space-like, traveling less as time-like, moving straightly's not the trick maybe you've heard the twins paradox gaveled. one rocketing far to Alpha Centauri, even prized Feynman got this incorrectly - the spacetime path distance that's traveled, not acceleration as the key. so how match those cones to normality, where coordinate time is all we see. a light-year unit shifts dramatically, while by second closes on horizontally, a surface like Newton's apparently. the beauty of unification arises full of various surprises: as length contracted, time stretched, a common origin fetched, energy and momentum unifying. but our vision is not yet complete, paradigm aligned classically, predicting where all the stuff will be. quantum mechanics is a strange treat, and merging gravity so trying.
It is ridiculous how perfect this entire series is. Thank you for giving the masses enough credit to teach us spacetime from the top down.
Even as someone who is educated on these subjects, I found this lecture very enjoyable and informative. You really have a gift for teaching.
"You have a twin, two twins that's what makes them twins." - Sean Carrol 28 April 2020.
Awesome intro to SR. I personally think 'the best way' (if there is a single best way, which as Sean says there probably isn't) to teach SR is to emphasize the analogy between Euclidean rotations along the unit circle and Lorentz 'rotations' along the unit hyperbola. People have a strong intuition for rotations along a circle, which they can use as a nice bridge to the much less intuitive Lorentz transformations, because really it's the same basic idea: make a transformation that preserves a distance. I also like this approach because it makes it easy to do a 'symmetry-forward' intro to the subject, which lets beginners see the power of symmetry in a simpler context that will then become useful as they advance.
Good god, this is amazing Sean. Thanks for teaching a Texan with a ged about the true structure of spacetime.
This is the one I have been waiting for, space time, a dazzling feat of the human mind, I hope I understand it better, its a difficult topic for a layperson.
To get a better intuition for how spacetime diagrams work in Special Relativity, especially the way the axes shifted and sort of "pinched together" for the person in motion (the technical term for which is "Lorentz Transformation"), I highly recommend Minute Physics' series on it. He had a physical device made that recreates the hyperbolic geometry of those transformations in a very visually compelling way.
ua-cam.com/video/1rLWVZVWfdY/v-deo.html
This is at least my fourth attempt to understand spacetime. This is the second video I've watch and I've also read about it at least twice; once was in Carroll's book "From Eternity to Here". I still feel like I only kind of understand it, so maybe I just don't have much of an aptitude for complex physics.
General relativity is a very difficult topic for any layperson when you have to understand the field equations.
@@alankoslowski9473 Think in this way: the trick here is that c is invariant i.e. c holds the same value regardless of the coordinate system from which c is measured. If you start to move, you will find yourself in a new time coordinate t' and in Newtonian mechanics the x' coordinate will be perpendicular to t' but in that case c will not be invariant. The only way for c to be the same in the two coordinate system is when the x' coordinate has the same angle to c as the t' coordinate. Therefore this skewed apperance of the primed coordinate system, which, in turn, creates time dilitation and length contraction. And yes, I'm more fond of the traditional way of teaching relatively ;-)
Thank You. This is just such a gift to us during the covid-19 debacle we're navigating through. 👏✌🤯💓
lifes debocle
Indeed
I enjoy all of your efforts and I have learned so much from you, quite painlessly too, I might add !
Thank you Professor.
"Nearest star is 4 light years away" dear God, he's been inside so long he forgot about our 🌞.
lmaooo
@@blackieblack Hmmm...you speak the true true. Maybe nico make joke?
@@blackieblack Ya ! As when you say "stargazer" ,you dont usually include those who stare at the SUN !
LOL! There is a part of me saying,, "He's talking about the closest star to our solar system ya moron!", but there's another part of me saying, "Ha! He's got ya there, Sean!"
I love that this series exists. If only the other people I'm with in lockdown watched it too, I would be able to have conversations with people about topics more interesting than the weather and tiger king.
I feel you dearly.
Can't get enough of these floating torso thumbnails.
The durian fruit is also much like strings in string theory. A person gets a stick and bangs on it to hear the vibrating beauty inside like the universe holds. Different vibrating sounds mean different tastes in each durian. They can be hard or soft in different variations. So the decision is not just 2 choices of I hate it or I love it. The people that hate it only smell it. The people who love it feel deep down in their soul. Something AI can never have. I doubt a human made machine, even one reaching the singularity could ever develop a loving nurturing soul. The durian analogy is way more complicated than the people in the podcasts implied, much more. When I see AI can do that I’ll be amazed. Until then it is just a robot. An object forced into slave labor.
Thank you Sean! Honestly, I think your top-down approach is more intuitive.
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I think Physicists would have been in a far better position if they had given a completely different name to SpaceTime.
I love Sean Carroll - he's one of those people who were just born to teach / impart knowledge.
Best lesson I’ve ever had in special relativity! What an amazing job! Thanks for all your work!!
These and Brian Greene's Equation of the Day have been a great way to review all the physics I haven't seen since university many years ago.
Thanks to all the scientists and mathematicians keeping us sharp with these lessons!
💯
also Closer To Truth
Didn't know Brian Greene was doing a series as well! I will check it out, thanks for sharing :)
🙃
Please tell me more channel
Love these videos -- the format is perfect -- the writing/drawing/grayboard sketches forces Sean to slow down, and pace the presentation -- love it!
Imagine Sean Carrol and Jim Al Khalili together in a scientific online school. The laymen applaud!
Sean you continue to create marvellously educational and inspirational content, thank you!
Watching a legend’s lecture!
This is the blessing of science & technology- you can watch the best of the bests from anywhere at anytime. 💟
Thanks Prof. Carroll, this lecture was amazing. I am very grateful.
While watching, I think I grasped why the doppler effect in radios occur (in ham radio, it happens when you communication with satellites in low orbits). And indeed in the wiki page en.wikipedia.org/wiki/Doppler_effect it says it's related to relativity! WOW! Before it was just a mysterious thing, now it (kinda) makes sense thinking in terms of the CONES in space time, and radio waves moving at the edge of the cone. I will have to think more about it.
But if you happen to do a generic Q&A, perhaps you can mention/explain it?
THANKS!!!!!!
Sean Carroll, I may be a Dunning-Kruger case, but I don't think so. Would you do me the kindness of granting me your ear for five minutes?
You're not stupid, you're sane. There's no proof for Minkowski's interpretation of the Lorentz transformations. Lorentz himself said time dilation is a real effect of clocks being slowed down when they move through the vacuum.
Photons and gravitons are not on all fours here in one very important sense. Photons are all around us while gravitons are hypothetical entities imagined to exist as a consequence of some attempts to shoehorn a successful statistical model of the microworld on to the very large-scale properties of extension and mass. It is far from clear the project of seeking a subatomical mediation particle for the force we infer from the nature of the motion through spacetime is well motivated, let alone that the particulate ontology of one of those efforts should be viewed as just another thing in the world, like light.
The universe is under no obligation to conform to our theories, no matter how preposterous they may be.
Otherwise, keep them coming - the videos, I mean. Thanks much.
You’ve improved my life immensely.
There is also another way to see that it isn't about the acceleration: The Fermilab channel on youtube did a video about this topic some (space-)time ago where they introduced a second spaceship flying towards the observer on earth. The two spaceships exchange their times while passing each other (without stopping) and the second spaceship arrives on earth with a shorter time than the observer on earth measured, even though none of the three observers ever accelerated.
Yes, that is an excellent video, I agree! ua-cam.com/video/svwWKi9sSAA/v-deo.html
In spacetime... no one can hear you scream about Euclidean geometry.
😂
You mentioned that people like string theorists often think about extra dimensions of space but still just one dimension of time. I'm curious whether there are any theories with extra time dimensions?
Mathematically it seems like it would be easy to add an additional dimension with a negative sign in the metric, but i'm having trouble thinking about what it would do to causality or anything.
Hi Sean, can you explain Why distances contract with speed,if your picture suggests the opposite?
Professor Sean Carroll, kindly suggest an updated book for "the biggest ideas of the universe".....theory + math both.....with required math.....Thank you Professor.
Sean, at 49:51 is it really x2-t2? I thought it should be the opposite - t2-x2, no?
I think it is because he is talking about length. t2-x2 would be about time.
Sir, you are one of the best lecturers I have seen. Thank you.
Thanks prof Carrol,
Finally I better understand some aspects of special relativity which was for me still rather vage and a bit confusing. Many thanks!
Allow me to ask a question a bit out of context. If gravity is a pure consequence of the nature and curvation of spacetime and not, as often said “a real force”, why do physicists want to unify gravity with the 3 other forces? Is it correct that gravity just seems to act like a force since the path of an object in a gravitational field undergoes a linear acceleration as a consequence of the shape of spacetime?
Thanks a lot.
Yes but what they want to understand is what causes the curvature.
Sean Carroll I cannot thank you enough for doing this. Going through the motion of knowing more and understanding less which is exciting.
Speed of light is not constant; it depends on gravitional field density.
Thank you so much for these! I just won your new book in a giveaway (thank you Matt Ingebretson!!) and I'm extra excited to have these lectures to keep me thoughtful while waiting for it to arrive.
Question: are there any theories that include multiple dimensions of time? or; is there a useful reason that we might consider multiple dimensions of time?
Thanks for the whole series!
not attempting an answer, but offering questions:
What if we approach this by (re-)asking "What is measured?"
What do we measure, when we measure "time"? Casual / informal / unpolished answer: "change" = the change of seasons, the change of the position of the sun in the sky, the change of growth in our children, the change in decay, etc.pp.
What do we measure, when talking about "space"? again casually speaking: the position of any given object as well as the distance to a reference point.
What I think "spacetime" beautifully does, is stating something painfully trivial: time and space viewed separately are basically cross section and longitudinal cut through the same cake, and it would be better understood if asking both when and where.
In this sense, time and space already are dimensions both explaining the same phenomenon. How would adding more dimensions to "time" help us understand this phenomenon better? or in other words: what could we add to "before" / "now" / "after" that would explain the overall phenomenon better?
@@kamiodd2873 Take to the left at 4 o´clock..
You could have a second time dimension in which the two together represent the world as experienced by you (your worldline) and all the other worldlines not experienced by you but which are also possible.
Sean, you are great communicator, if you were political I would vote for you.
What does the spacetime diagram look like from the perspective of the traveling twin? It’s unclear how the symmetry is broken
Looks you are only one watching with attention. Twin paradox is not what Sean told us. Just see wikipedia for a start. I devised a solution in SR, just lazy to publish, plus I'm not sure my solution is original.
52:35 "you send out an infinite number of little rocket ships travelling at faster than the speed of light, at infinite speed, of course you couldn't actually do this" - disappointed.
45:05 I've heard a guy online propose that Time has multiple dimensions (just like space). Seems like nonsense, but is there any credibility to this?
Thanks for a great video. My question is about whether space-time is taken as a physical concept or as a measurement framework. In GR Einstein seems to define space-time as resulting from what one measures with a ruler and a clock; how is it defined in e.g. QFT? In GR it seems that space-time is dependent on the energy-momentum structure in space-time, so it is sort of implicitly solved. Are the fields in space-time the source of space-time? Personally it seems to me more satisfactory to think of space-time as a non-physical framework we use to order our perceptions and measurements, somewhat like a 3d spreadsheet.
Time causes space to expand. Time uses energy from the universe, causing the universe to expand and the moons orbit to become longer, the moons orbit moves farther from the earth. Time is a measure of the entropy of the universe, of space.
Thank you for doing these Professor Carroll, such an interesting series of lectures. I look forward to each and every one!
These are so excellent! Thank you very much for doing this!!!! I wish everyone was as generous with their knowledge & expertise. Thanks again!
Great video very educating! I have a question that if space=V*time, then you said light speed is the limit. But what if something travel faster than light? Will this equation cause more space to be created if speed exceed light speed and does that mean something could reach other space dimension if it travel faster than light? Thank you!
Excellent video, I liked your „top down“ approach very much! Thank you!
Thanks for this great lesson, but i am still struggling with a question regarding the Twin Paradox: what if space is positively curved and the universe is closed? The one twin starts the journey with the rocketship and is travelling just in a 'straight' line all across the universe. As space is positively curved and closed he would just arrive at where he started his journey. How could it be that only the twin who is travelling is aging more slowly? Arent Both, the twin in the rocketship and the twin staying at earth, in an inertial reference frame? From the persective of each of the twins, the other is in motion and time should tick slower compared to the 'stationary' twin.
I am confused
I think the trick here is that you have to undergo an acceleration to experience the time dilation relative to the stationary twin. So since the stationary twin never moves in his own frame of reference he never feels an acceleration. The twin you postulate moving around the closed universe had to undergo an acceleration to make the trip. Hence his time is dialated with respect to the twin who never moved. Even though it looks like the stationary twin moved from the perspective of the twin who made the trip, he really didn't move because he never underwent an acceleration. Whew...... that was a long explanation, but i think I'm correct.
This is absolutely great, the way you explain these physical concepts/idea's is just soooo good and understandable! Thanks for doing this!
Thank you so much in making this simple enough for anyone to understand... well, maybe not for Trump.
_Definitely_ not for Trump! Heh, heh.
I think you'll find Donald has a beautiful understanding of spacetime; one of the greatest most beautiful understandings of it ever, and he's going to do more to understand it even more beautifully great than anyone ever, by injecting it with beautiful sunlit disinfectant, grabbing its genitals and building a wall around it. Covfefe
Is your life that very Petty , that you need to introduce politics into something that could not be less related to politics? I will pray for you.
Dear Prof
Carroll, please can the quantum vacuum fluctuation exist inside black holes (at singularity) ??
Thank you sir :)
Loving these videos. May our light cones continue to intersect.
My new favorite expression.
55:49 wow that blew my mind getting to see it that way
I'm not sure whether I feel smarter or dumber after watching these videos. I'd watch them more than once, but I'm afraid I'd figure out which one it was. :)
In America the speed of light is one foot per nanosecond - about accurate.
How did we become confident that c is the correct value of the conversion factor ?
So, if there is no simultaneity, does this apply to causality too? Specifically, does this in anyway, explain the delayed choice double slit experiment?
@@blackieblack thank you for your response! So paraphrasing what I understood, if we improve the detectors to be more efficient and move the pattern detection screen further by orders of magnitude, can we glean any new knowledge?
I don't understand how this doesn't have like millions views, this is the most interesting thing in the world and mr. Sean is such a great talker, thanks for sharing what goes on in your genius brain 🙏
Sean is a wonder of our world, that expands our perspective, however complicated it may be...awesome work Sean. I've seen a good portion of your online videos, always captivated, as I crave the amazing guidance and understanding you bring to theoretical, and traditional physics.
Sean, you are a nice person but you do not understand the Relativity! On ~18:00 you say Feynman was mistaken to say that Time Dilation caused by acceleration. Feynman was absolutely right! You are mistaken by saying Time Dilation is caused by traveling distance! Just imagine two two clocks, stationary relative to each other, at different heights on the Earth. For the higher one there is more Time Dilation, and it is only because of different accelerations. No traveling distance is involved.
As you move faster through space you move slower through time.(velocity based time dilation) As you move closer to a large mass you also move slower through time. (gravity based time dilation) While it's true you had to accelerate to achieve a faster velocity through space, the effects don't stop once you stop accelerating. Agree?
He was talking about the Twin Paradox. It is possible to set up the experiment where no acceleration is involved (by having an inbound and an outbound traveler) and the twin back on earth will still age more. The difference is the two different reference frames of the travelers versus the one reference frame for the person on earth.
thank you so much please continue with this that course was priceless the top down point of view that you exposed was extremely convenient for me because I needed a tidy framework to organize what I knew and understood about relativity and this is just on point
As someone who grew up with more Buckminster Fuller geometry than Euclidian geometry, your "I'd rather do it this way" approaches are much more accessible to me; I like when you go there. I finally get relativity, since you are willing to move away from the x, y, z coordinates into a language that is more spacetime friendly. Thank you!
Really great videos. Thanks. It would be nice if in your Q&A could talk about the special case of photons and how they "see" the Universe and (not) experience time (also maybe in the context of their interaction with other particles, e.g. in the photo-electric effect, when they "appear/disappear")
Hey Mr Carroll. Multiverse is true because particle small enough to be in a quantum state is an universe in it self. When you use calculus in Feynman diagrams, you connect relativity and quantum mechanics.
Are we always traveling at the speed of light through spacetime no matter what our speed? How you were describing Minkowski space reminded me of this blog post:
medium.com/predict/we-all-travel-through-spacetime-at-the-speed-of-light-d60cb389dfc2
Omg I didn't know you had a YT channel. I love watching your talks
How certain are we that the speed of light is invariant throughout the entire history of the universe. Like just after the big bang was the speed of light the same? Is it impossible to know?
I always wonder what it'd be like to be a photon. If length contracts as you approach c, and photons travel at c, then how big would a photon think itself to be from its own frame of reference? Infinitely large? Is that the flip side of considering how a photon experiences zero time for its entire existence? If I were a photon, would I ever even feel like I existed at all?
I would also love it if Star Trek showed the Enterprise shrinking smaller and smaller as it approaches warp. Little teeny tiny toy spaceships zooming past a gigantic hydrogen atom.
Well, the length contraction would only happen along the direction of motion. So assuming it moves in a straight trajectory, it'll only shrink in that one direction and effectively look like a giant pancake at warp speed.
@@incoathwetrust4612 And the contraction is for an observer.
Great stuff but is anyone else hearing excessive hiss in these videos?
No the audio is good
Time to put on a fresh pot!
Sean is very pleasant and interesting to listen to. Thankful greetings to Sean for having these lectures!
In the space lecture you mentioned possible extra space dimensions on top of the three we experience. Could there be also more than one time dimension?
Did you watch the time lecture?
Is this series leading up to a new book?
Not sure about your explanation that it is not the acceleration. In your spacetime diagram, the two observers accelerate for the same amount of time, but that is only in that particular reference frame - the global frame where the twin was mostly at rest. If you looked in the comoving frame of the twin who ages less, I think he will see the times for the accelerations as quite different.
One can of course analyze everything from the point of view of the twin who ages less, during the first outbound leg, he will indeed age more (usual special relativity calculation), but when he accelerates, he will observe a gravitational field, and then see the second stay at home twin age more because he is higher up in a gravitational potential - and then during the inertial return trip he will age more than the stay at home twin - combining all the effects leads to the same special relativistic result of the stay at home twin.
I think what you say is partially correct, in that it is the large distance separation and thus large effect of being in a higher gravitational potential, that causes the stay at home twin to age more from the perspective of the accelerating twin.
Thanks Sean for these great videos.
Wait.. so you can theoretically have more than one dimension of time?
10:26 Thank you for that information!! When you put it on a grid like that, it becomes clear (rather, it did to me) that if you have and x and y Axis, and two point, the line or path is the slop...but, if time isn't included, then we are just measuring distance (rise over run in units relating to linear space only).
When we change our vertical axis to represent time, we know get more useful information. Our slope is still rise/run but now it's:
_time(duration)/space(distance)_ instead of *space in one direction (distance)/space that is 90° off in angle of direction (distance)*
Now, we can see the time it takes to travel a certain distance of space (using whatever units we choose to use, so long as it's constant: light-years, MPH, whatever).
When that spacetime is curved, then using just space to find the shorter path from point A to point B is (as stated) "kind of like" walking up to a valley and deciding that the only way is to walk down, through and up the other side of the valley... when, if you had the ability.... flying across would take less time, even if that meant having to do more work (more events) than if you had just walked. You have to get the plane ready (fueled up, know where you're going to land, do a ton of preflight work), take off, fly that short distance, land and put the plane away.
Intuitively, it seems like walking is less work and the easiest way to get from point A to point B..... but, if the time it takes to walk there is longer than it would be to go through the work of flying there, then the reality of the situation is: the shortest path from point A to point B, considering the time each choice (walking vs flying) takes, might be a longer path through space.
In other words: walking would take less steps (events) and you would walk fewer miles, but you would take longer, making it the longer of the two routes time wise.
If you flew, you would have to go through considerably more steps (events) and your path, including the flight, might be a longer distance of space covered. However, if you covered more space in less time by flying, then flying would be the shorter of the two routes, time wise.
It's similar to space in that flying would be a straight line through space, making it the shortest path... but in space, most of the time... flying over a valley isn't an option for us 😂 so, it's kind of like space, like you said, but the shortest path through spacetime might be through more space than time. You get there sooner than just covering a straight line in space, but you end up covering more space...just in less time.
Makes way more sense now! Thank you! 👍🤘
Awesome presentation Prof. Carroll. I'm very impressed with these casual videos you are doing. Question: Your last written statement, "General Relativity: Spacetime is dynamical, responding to matter / energy. => Gravity". Since we cannot measure space, time or space-time without physical tools made of matter / energy. Wouldn't it be equally true to say, "Matter is dynamical, responding to other matter /energy nearby => Gravity". The point being, we can't observe empty space-time, we can only observe its effects on the observable matter / energy it contains.
I keep coming back to my highschool physics classes when they talked about the difference between distance and displacement. I know they are different but how significant the difference is is not so intuative
12:45 "Shortestest....thats not good..." LOL
Outstanding as always. Sean, if you recited the phone book I still tune in. Thanks.
I think I'd have a better chance of _understanding_ the phone book. Hey, I know he does his best, but the phone book is about my limit, I suspect. :)
29:00 3 seems like a clumsy number, what would happen to our maths if the speed of light was 1 instead? i have wondered for ages why the circumference of a circle is such a weird number, i joke that it's the registration number of our universe, a different universe would have Pi as a different number, and i wonder, is our universe is bent, could Pi not being a round number be due to "our" circles all being warped? it's okay, i am on drugs. but to get back, 300,000,000 meters per second, would maths and cosmology still work okay if we made it 100,000,000 - surely our numbering intervals are based on the the amount of time it takes to get round the sun, but the actual length is arbitrary?
while i am here, i was watching one of the debates, with the bhuddist (wallace?) and he kept remarking about how we do not understand consciousness, and one thing that has bugged me is the feeling of why am i here now? we talk about what a great era we live in, the music, landing on the moon etc etc, and it got me thinking, why is my consciousness conscious NOW? surely a conciousness could appear in anyone - i could have been born someone else (if you see what i mean) born someWHERE else, but also, why at this time, surely my consciousness could awaken at any point in time?? however, after watching sean's talks it makes me realise this is daydreaming rather than physics, my consciouness can ONLY be here and now, whatever it is that makes me awakw compared to a rock is still just physical, it is not separate from time and space.
I, aka Sean, preferred to start from scratch. If you simply start from scratch and analyze "Motion", and do so properly, you will soon discover SR and all its causes or its foundation, which brings it about. No knowledge of Newtonian physics is required to do this. The less you know about physics, the easier it is to discover SR all by yourself.
I’m not sure our model is correct.
There is no evidence that time is scalar, I have never seen anyone or anything be anywhere except the present. Granted the light from their present takes a while to get to my present, but light can only move one Planck length per Planck second, and the Planck are very small if gravity is strong so it can take multiple plancks seconds for me to observe what happpened over there.
Neutron decay cosmology is the physical process solution to black hole information paradox and fine tuning.
What about unavoidable conscious computations resulting from the acceleration. We have the motor and sensor homunculi which will always map the input from our sensory stimuli and it has an analog input since our blood is incompressible and has a mass, viscosity and so on. The electric signals will always be directly correlated to the fluid flow and its mass will always respond to a force and thus J/m. Unavoidable energy into/out of our system as a result of the change in distance distance.
let me start by saying I dropped out of high school in 9th grade, at 36 i went back got my ged, and now at 40 im watching this brilliant teacher and actually able to understand some of this lol, good job Mr. Caroll big fan of your many worlds stuff too!
If the galaxies are accelerating away from each other at a faster and faster rate then that means humans live longer now than they did in the past directly because of that?. Or is our galaxy moving on a straight line trajectory with a constant time lapse?, but then the galaxies and universe itself is not accelerating if that's true?. I think I really misunderstand it because it seems that if speed/acceleration effect time and the universe is expanding faster then human avg life span should have a direct correlation to the solar systems accelerating speed through distance even if on a conceptual straight line?. Maybe I am making a very naive maybe childish assumption that our solar system holding us can act as a big spaceship through space-time?.
I very much enjoyed the little "psshhht" for the rocket-ship 8)
There is a type of Space-Time diagram in which the scale for both systems is the same. They are called "Loedel Palumbo Diagrams" and with them any analysis of special relativity is significantly simpler. They were developed in the mid-20th century by the Uruguayan physicist Enrique Loedel Palumbo from the simple, but brilliant idea, of considering in a diagram of Minkowski not one, but two "mobile" systems with the same speed, but in opposite directions and then remove the "fixed" system from the middle and... voila! you have two systems with the same scale! .The relative speed between these two systems is now given by the sine of the angle between the axes, not by the tangetic and trigonometry is that of all life. It is a shame that they are not very widespread.
This is a link to the demo
ua-cam.com/video/o4kKeG8PyyM/v-deo.html
The Chinese use this word '宇宙' (pronounced 'Yu Zhou') to refer to the universe. It's a compound word that can be traced back 2,300 years when the first recorded use was by a philosopher Shi Jiao (c. 390-330 BCE) in his book Shizi. He explained the word as such: the first character 宇 means 'up, down, and the four directions' (上下四方曰宇), while the second character 宙 means 'ancient, past, present and future' (古往今來曰宙). If examined from a modern standpoint, his view of the universe as a whole was exactly the definition of spacetime, because he already combined the concepts of all directions (space) and all tenses (time) into a single notion. These guys must be onto something!
so do people at the equator experience less time than people at the poles? (given that the equator is going ~1000 mph?) do people near the equator die at younger age, since they exhaust all their "biological potential" relatively more quickly than people at the poles?
Electrons, like atoms, and black holes, and the universe as a whole, are horn toroidal fluid vortices (hence "point-particles") in/of the single, scale-uniform 'super-fluid' medium (I call it the SUM, a.k.a. "space-time") whose self-relative motion (a.k.a. "acceleration"; "momentum"; "push") as vortices and waves, comprises the evolving (hence "time") structure of the universe and all of its content "physical objects". Therefore we can say that the "material universe" is 'pure motion' (primarily point-radial in trajectory). The Einsteinian "time dilation/ length contraction" principle applies to the SUM itself, meaning that its self-relative motion ("acceleration" as 'motion relative to itself over time') is the mechanism by which the otherwise absolutely homogenous SUM 'self-differentiates' into the structural diversity of the observable universe, including our own bodies.
Also, therefore, not only do massive objects "curve spacetime", massive objects ARE "curved spacetime". The inflow of the SUM equals the point-radial outflow "expansion" of the SUM compression wavefront that is the surface of the mass-object (e.g. the Earth). Ergo the "gravitational (and smaller scale) field(s)". Since SUM fluid vortices, and every complex manifold thereof, including ourselves, constitute 'I/O devices' (inflow/outflow; input/output; positive/negative; "yin/yang"; etc.), we can say that the physical universe is comprised by an otherwise, absolutely continuous SUM "simulating" (by means of its self-differentiating, self-relative motion) a "discrete particle" - based "material universe" as "a universal self-organizing network of distributed I/O devices" which are manifested in terms of their inter-communication by means of the specific sequence of SUM 'vibrational acceleration waves' traveling at the "constant, finite, but asymptotic limit for all mass-objects" speed of light which they emit and absorb. We "human beings" are momentum routers ("pushers" of "things") in that network. In order for there to be a "push", there must be a "something else" to "push against". "Yin/Yang". Consider that every "sensation" - i.e. that you are "conscious" of - is comprised of a "push" (or vibrational series of "pushes") at some scale, at some amplitude, in some 'direction', as a "transfer of momentum"; a displacement of a mass object from its otherwise geodesic path. So the "material universe" is apparently a self-configuring momentum-routing circuit /network. "Consciousness" is 'a self-configuring momentum waveform' in/of the SUM.
P.S. "Dark matter" is the SUM itself concentrated around its "material" vortices, and "dark energy" is its larger-scale flow.
ua-cam.com/video/MmG2ah5Df4g/v-deo.html 0:22/11:57 They are being carried along by the outwardly expanding flow of the SUM (scale-uniform medium) itself from its horn toroidal fluid vortexual architecture "output". They are not, themselves "accelerating" (undergoing "proper acceleration") by means of an 'on-board' power supply. Thus, in this case, they are not moving "through space over time", they are moving "with space over time". Light waves are the universal 'CPU clock ticks' of 'time'. They make up the 'Cartesian coordinate system' of the 'space-time epic' in which we are taking place. ...
Call the Y axis "time", and the X axis "space". Let your eye be at 0 looking in the positive Y direction, and let any other detector be placed anywhere else along the X axis. The photon (or physical increment of "time") is propagating toward your eye, or other detector, as a spread-out 'shock wave' front, and collapsing point radially toward its detector, only being "detected" when the momentum (acceleration) pulse it is transferring through the SUM (scale-uniform medium, or "space-time") literally from its horn toroidal 'point' of origin is transferred to its corresponding destination point of detection.
The universe might be described as a 'self-calculating quantum computer'.
Let's discuss: ua-cam.com/users/onemediuminmotiondiscussion
Around 10:25: What if point B is directly above A in the spacetime graph? i.e. you don't move at all in space, but only in time? how do you take various paths through time?
Hi Sean and thank you for all your videos (BIU and Mindscape etc), I find your openmidedness to be wonderful and informative. I just watched episode 6 of BIU and I have 2 questions please. 1/ As we understand it, at the start of the big bang, were there massless particles traveling at the speed of light or did we have to wait until photons came into existence? and 2/ Do we know how many light years we are away from the BB and therefore (given the light cone from the BB) how much further past us the cone currently extends? Thank you - Jamie
I'm a little confused. @50m it's written: l^2 = t^2 - x^2
from Pythagoras, it seems it should be: l^2 = t^2 + x^2 or am I missing something?
Sean says of l prime "it actually has an extent in time...therefore it is in fact contracted." Which implies it is l^2 = t^2 - x^2, but I don't get it. Maybe it has something the fact that the "shorter" l prime looks longer than l (when it's in fact shorter). Probably an effect of this simplified diagram. Anyone? I guess I can't apply the Pythagorean Theorem, but must instead use the "Minkowskian Theorem".
From 22m: elapsed time, (tao, T): T^2 = t^2 - x^2
From 50m: elapsed space, (length, L): L^2 = x^2 - t^2
is this to say elapsed time (squared) is the opposite of elapsed space (squared): T^2 = -L^2
or even T^2 = (Li)^2
I thought I was coming to understand spacetime, but now so many questions....
I sometimes think, since I don't have the math background to even START to 'know' about relativity 'completely', (actually, I guess that means I ALWAYS think that), anyway, not having the math background, I think that by getting as many different versions of the explanations (for the layman) of relativity as I can, that I'll get more of a 'kick' out of the downright cool aspects of the subject. Well then that means I have to say that the two or three minute explanation of "length contraction" given in THIS video is by far the best one I've seen, in that it allowed me to integrate all the other explanations I've heard in a way I just can't adequately describe. It was truly so succinct and clear, in the context of this group of videos, that I feel my understanding has taken a 'quantum leap' after absorbing it. BRAVO! AUTHOR!! AUTHOR!!! :-)
Professor Carrol. Thank you so much for explaing things in a clear manner.
I have a question that is naive..
If the energy of × is quantum, is the speed of lights energy up to 10 out of 10 on the quantum scale?
As in light has reached the maximum charge?
I wonder because how can red and blue light shift occur?
No doubt you have covered this subject many times. (Got a link?)
I am very interested in your top down approach to teaching. At school learning was difficult as it seemed to have no practical applications..
Maths was extremely tedious, and I think its the teacher not the student that trail blazes your enthusiasm.
As a fan boy I have bought your book Something Deeply Hidden and was hooked.🤓
Why is the speed of light the fastest, well, let's say that light is actually moving almost exactly at the speed of time itself, then there-for Light experiences nearly 0 time. So even if it takes 5 minutes of light to reach you, in your perspective, it takes time 0 second, or (0.000000000000000000000000....1) seconds. Then in that case, if you actually travel faster than light, you would need to technically travel backwards in time. You're welcome again physics. But again, it's all theories. You need solid testable proof from tons of readings and observations. Ect. Otherwise it's all fancy sounding guesses, aside from applicable sciences. Also traveling while experiencing 0 time (moving exactly as fast as time moves) would look like a straight line horrizontal on your t / Xy grid. So you see you experience no time because you are moving just as fast as time, so there-for time is not "Passing you" physically, because time is actually a motion itself.... now that'll mess with your mind. If you observe time as a substance that's moving. Gives a whole new meaning to '"space"time'
I tuned in during covid on almost all of your streaming lessons. Later I decided to copy these streaming versions of your biggest ideas to watch again so as to get better notions of the topic. The stream I think are much much better in terms of understanding these difficult physics subjects. (I think the books are for coffee table conversation pieces) The original streaming with the diagrams, the math, the explanations are what got me past the dark muddle and feel I have an even better grasp of these topics. This stream on the time cone when shown with the coordinate explanation really is the turning point for me understanding spacetime. The college level courses in calculus (differentials and integration) which I struggled with also was a huge help when following your streams. But it gets bumpy by the time we get to quantum physics.
On the twin paradox. Let's say the two twins are A and B, or Ann and Bob. Ann stays at home and Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years pass. Bob returns at 3/5 light speed, again taking 4 years. Ann thinks 10 years have passed, and Ann and Bob agree that Bob is two years younger. The confusion arises not because there are two equally valid inertial rest frames, but because there are three. In special relativity there is no acceleration to speak of. The three inertial frames are 1) at-home twin 2) the going-away twin and 3) the coming-back twin. It doesn't make any difference that the last two are physically the same twin. They still define different inertial frames. An important question is what is the relative speed of the two Bob frames? On first glance, it might appear that one is going 3/5c in one direction and 3/5c in the other direction, so that the difference between the two frames is 6/5c but special relativity does not add speeds this way. The actual difference is only 15/17c, fast but not faster than light. Now, since special relativity lets us use either rest frame, we assume Bob is the at-home twin. Ann speeds away at 3/5c. No problem so far. But after 4 years of waiting, Bob must change his inertial frame. If we allow Ann to return, we've only restated the problem with the names switched. In the first version, Ann stayed in an inertial frame, and she must stay in an inertial frame in this version. Bob zooms off after Ann at 15/17 light speed and of course catches up. It takes him 4 years, and he has seen 8 years since Ann left. Ann has aged 10 years. You get the same result, and there's no paradox.
Spacetime-ly
we'll circle back to an energy ride,
but first let's talk more classically
about spacetime and the limit C.
why the idea of union counts aside
from space and time as separately.
it's really about relativity,
theories special & general clearly.
we'll be presenting top-down Minkowski's 4D
(not starting with Newton's universality)
then get back to how everyday we see.
gone Newton's space and time so absolutely,
not just adding a coordinate to three,
when we travel from point A to B.
a new structure mathematically,
paradoxes go away conceptually.
how is going A to B in some ways
like traveling along in space 3D?
a clock's elapse not coordinately,
and light cones demonstrate how spacetime plays,
all proper time intervals will agree.
(but order may not so easily
if moving non-inertially)
[chorus]
spacetime's a dynamic,
there's no need to panic,
when shifting into space-like,
traveling less as time-like,
moving straightly's not the trick
maybe you've heard the twins paradox gaveled.
one rocketing far to Alpha Centauri,
even prized Feynman got this incorrectly -
the spacetime path distance that's traveled,
not acceleration as the key.
so how match those cones to normality,
where coordinate time is all we see.
a light-year unit shifts dramatically,
while by second closes on horizontally,
a surface like Newton's apparently.
the beauty of unification arises
full of various surprises:
as length contracted, time stretched,
a common origin fetched,
energy and momentum unifying.
but our vision is not yet complete,
paradigm aligned classically,
predicting where all the stuff will be.
quantum mechanics is a strange treat,
and merging gravity so trying.