When I saw Pythagorean’s Theorem appear showing the relationship between time and space I had a religious experience. I am now one with the universe. 😌
I had this 'almost religious' moment in the first time I learned that a mathematical instrument invented thousands of years ago, was used to discover something so complex.
Irata, if you see this comment, (1/gamma)^2 + (v/c)^2 = 1^2 not only is this a^2 + b^2 = c^2 (pythagoras) this is x^2 + y^2 = 1, the unit circle. The big man. The circle of circles. also, the '1' has no units. Pure 1 goodness, chilling with time dilation and the speed of light.
What you saw there was someone assume a theory to prove a theory. It was assumed that light can travel no faster or slower than c. It was also assumed that time is not universal so we get time dilation in addition to length contraction. TD is a false concept! It is mathematically unworkable.
I'm a Mathematician and would love to see your take on some classical equations (Euler identity, Riemann zeta function and such). But if you intend to go on this Physics/Relativity path I suggest two topics: 1) Talking about surfaces, curvatures and a conversation about the Gauss-Bonnet formula (Relation between topology and geometry, genus and curvature); 2) Talking about the inverse square law and the way it manifests in various laws of physics (Gravitation, Electric potential and others). This has been great, hope you do many more of those.
@@vijay_r_g He first used the famous equation for velocity V=ΔS/Δt Then he manipulated the equation to get Δt = ΔS/V And then he applied to our case. Note that in our case the velocity in both Δt and Δt' is C, the velocity of light, so when you make the ratio they end up cancelling each other. I hope it was understandable. :)
As somebody who doesn't know physics, I'm confused at if tm < ts, doesn't it also mean moving L is smaller than stationary L (since L=tc)? which means the moving world is smaller??
Hello Sir, thank you so much for making our time worth by such beautiful explanation. I am a Physics student from India. I would urge you to kindly make a video on the Einstein's Field Equations and GTR as a whole. Thank you so much.
The simplest and most unique explanation of time dilation I've ever seen... Thank you so much for creating for us this daily reminder of why physics is so beautiful and astonishing.
I thought I was fairly well versed in physics but I really don't see what speed has to do with time. In the example of two light clocks. These are closed systems the speed of the light doesn't change and the distance between the mirrors don't change. From the clocks point of view nothing changes. One on Earth traveling at some set speed and the one on a ship traveling close to the speed of light. How does the clock care what's going on outside of it? It's a closed system and nothing in the system changes.!???
@@rayhaney7143 your perceived time doesn't change while you're moving but you and that clock are made of matter and energy which is effected by spacetime. Motion is defined as the difference in the change of position that occured within some time interval. Classically speaking, you cannot move without changing position and you cannot change position without going through time. The clock measures ticks and tocks while the speed of light cannot physically change. However, the velocity of the clock itself can change and if the ball of light stays in the clock as it moves then you can see that the ball of light would have a longer distance to travel from tick to tock. Since the speed of light remains constant there will be fewer ticks the faster the clock travels.
@@rayhaney7143 From each clock's point of view nothing is different since they are in non-accelerating frame of references. However, one observer looking at the other observer's clock will notice time dilation. The concept applies only to different frames of reference moving relative to each other. I see my clock ticking right, you see your clock ticking right, but from my point of view your clock is ticking slower, because it is moving and light has to travel a longer way to reach the upper or the lower wall of your clock (the walls of your light clock are moving very fast away from the light wavefront).
I want to take a moment Brian to thank you for the comfort these videos bring, lending a sense of normalcy through the stunning wonders of Mother Nature, to these crazy dangerous times we find ourselves in. For me you have ALWAYS done this, as I suffered through a lifelong illness of the mind. You and other great science communicators - such as your guests at World Science Festival discussions and others, brought me into the world of physics and science where my own difficulties were put in proper perspective against the backdrop of our majestic universe in all its glory and gob-smacking wonders. Then as now, here you are providing light in the darkness, amazing mysteries, theories and the power of empirical scientific method. In a world of fake news and trigger-pushing TV, how reassuring it is to have peer-reviewed and tested information, much from the shoulders of the giants that came before (Sagan, Einstein et al). How comforting you’ve been for me through the decades you’ve been reaching out with your great talent as scientist and communicator. Even now. My thanks have been too long coming, but while we’re all locked away in our homes or on the front lines of this battle, we can tune in to tried and tested truths to reassure and comfort us. Or just give us pause about what our priorities are, or even just to know that while Earth faces the biggest peacetime threat since 1919 we have so much to be amazed by and grateful for. No virus can Ever beat that. Thank you 👌👏🥰🎋🌿🦋🙌🏾
It is the same equation in principle(pun intended)...think Einstein’s equivalence principle...gravity and acceleration are indistinguishable or ‘equivalent’...let’s not try to over complicate some seriously complicated shit🤪🤯🤔
Once again, Brian, with the current pandemic, how about an analysis of the general logistic equation? Particularly the differential form, but also the integral. It would be a very useful contribution to public understanding if done well, I think. Love the concept behind this series, thanks.
Thank you again, sir. I remember an airplane experiment confirming this. I just looked it up and find it is the Hafale-Keating experiment (on Wikipedia), 1971. like the laser measurement of distance to the moon, it's nice to have experimental evidence demonstrate the irrefutably logical.
I would like to see a video on the Twin Paradox. One of the explanations I found says that the difference in age comes due the acceleration (General Relativity) that the twin on the rocket ship experiences when he turns around to come back to earth. This acceleration is not experienced by the twin on the earth. I'm not sure if this is the wright answer, or if an explanation for the paradox can be given completely within the realms of Special Relativity.
It’s three years later and this is the only comment I can see addressing the twins paradox. Your explanation is completely correct, I think. The twin on the spaceship has to turn around and come home which involves acceleration and special relativity can’t deal with acceleration.
Dear Prof. Greene, thank you for an excellent explanation of the Gamma factor. I have recently started reading your new book - "Until the End of Time" - and I am thoroughly enjoying it. May I also express my gratitude for the "Quantum Leap" episode, in the Fabric of the Cosmos TV series. That is probably the best ever visualisation & explanation of the Schrodinger Wave function, that anyone can ever see.. Thanks again and please keep up the great work. Best wishes from Paul C., on lockdown in West Wales !!
I'm a 4th year undergrad in physics and I have never fully understood time dilation until this explanation. I've watched other videos on it and now I truly understand. Thank you
as a 4th year student, have you thought that it was suspicious that a v/c of 0.5 gives a gamma of 2/root3, and a v/c of root3/2 gives as gamma of 2? smells like... sine and cosine of 30 and 60 degrees, no?
there's another hidden pythagoras in the gamma equation; I recommend taking the inverse of gamma, 1/gamma= SqRt(1 - (v/c)^2). Square both sides and add (v/c)^2 to both sides. Another pythagoras.
Sir, I great fan of yours, the way you explain the complicated things in simpler form is awesome. I have request if you can present something on Nibru.
Awesome professor. That's the true elegance of physics. Unfortunately many physics lecturers miss this wonderful opportunity, as being seen in India. They just don't care about it's elegance, just memorizing everything. The Indian have ended up thinking Engineering is the best and nothing could exceed this, but it is just because they doesn't know about theoretical physics.
I think the time dilation derivation can be simplified: The stationary observer measures time for horizontal distance of the moving light clock as vΔt, but he also measures the same time for diagonal distance L’ as c Δt. As for the vertical distance L, it is measured by the moving observer as c Δt-moving. (I.e., the time he measures on the moving inertial frame for the up and down trajectory of the light). Applying the Pythagorean theorem the dilation relation follows between Δt and Δt-moving. So no need to assume L’/L = stationary time/moving time proportion before hand. Am I wrong professor? Thank you for all you do for the general public.
Super, Brian. Regarding the twin paradox time dilation not being applicable to the twin on earth: Is this due to the space bound twin's acceleration to close to the speed of light? What about the subsequent deceleration on the that twin's return to earth?
Brilliant presentation... I finally understood how time and space are related... It seems now so simple... Before it was like if I could not understand that the earth could not be anything than flat... Thank you.
One of my favorite equations is the one for exponential growth and decay. I always was thought that it was awesome that one equation could be used to calculate compound interest and the growth rate of bacteria. I think it's also pertinent equation for our current situation.
I know this is three-years-old already but I just bumped into it and I loved it, my question is - of course - about time travel in this specific equation, so what you've established is the theoretically you can time travel in the future if you travel at or near the speed of light, what I also understand is it has been established that the universal speed limit IS indeed the speed of light, the question is that if by any way it is possible to exceed the speed of light, would time theoretically go backwards? Or maybe the speed of light is sort of the highway on which time travels so it doesn't matter YOUR speed just how fast you get from point a to point b on that highway?
Took and online course with Larry R. Langerstrom [Stanford Univ.] on Understanding Einstein's Special theory of Relativity. Had I not had this course, I'd not be ab;e follow Greene's math . It was done at a much slower pace than done here. Leading clocks lag!
Brian, you are the most brilliant science teacher that has ever lived! Perhaps you can help me with this question: Of course special relativity has been confirmed by several experiments.Could we also explain the results of these experiments with Lorentz theory of light, if only we choose to believe in a more complicated theory? Thanks!
thanks proffessor Greene you really made those theories interesting and simple to understand, it would be really amazing to watch your explaination on one of the best equations you have discovered during hunt for superstring theory.
Hi Brian! Kevin here. At 18:24, you said if we grew up in a world that had our daily activities at relativistic speeds, we would have better appreciated the effect speed has on time. However, I think that may not be totally true because we'd equally be used to that particular scale of time if we existed in a relativistic world. It may even be more difficult for us to appreciate Time dilation in such a scenario since we may have to be moving at slower speeds to observe how time moves faster for such cases; just because we may not be able to get any faster since we can't get faster than light. Just my thoughts, Prof. I hope you understand my suggestion
Thank you Professor Greene for your explanation of a very difficult topic. I commented to ask what website has the clock differential demonstration. It's a powerful way to demonstrate the effect.
A fundamental yet little-known equation of special relativity is: s4 = c3 where c3 is the speed of light through 3-dimensional space and s4 is the speed of anything (including light) through 4-dimensional spacetime, and furthermore it's a constant. The equation implies the following: 1. Light doesn't age (its speed through time is zero). 2. Anything that travels faster than c3 through 3-dimensional space must travel backward in time. 3. Assuming nothing can travel backward in time, nothing can travel faster than c3 through 3-dimensional space. (A famous inequality.) 4. The faster anything travels through 3-dimensional space, the slower it ages. (Also known as Time Dilation.) I think s4=c3 should be taught in any course on special relativity. Although c3 is widely accepted as a "fundamental" constant, perhaps s4 is what's actually fundamental.
profound truth explained so beautifully and simply! the use of Pythagoras theorem is a key point in this model, but what for Non Euclidean geometries? examples?
I have a very silly doubt Dr. Greene. I seem to understand it but when I think deeply I tend to get confused. So here's my doubt:- Since the speed of light is constant and a larger distance needs to be covered in the moving clock from our perspective, then a larger time should elapse covering that larger distance in the moving clock compared to the stationary clock. That means time should elapse faster in moving clocks. It would be very helpful if you could clear this silly doubt of mine. Thank you, Sir!
1- On the constance of the speed of light, is it a hypothesis, mathematical conclusion, experimental results or all combined ? 2- When deriving the equation, why assuming the space is Euclidean ?
Adama Diallo it’s all of them, the speed of light started as a theoretical anomaly but has been experimentally verified over and over again. It’s definitely far beyond a hypothesis, all of Einstein’s physics is based on the constant speed of light and it’s all experimentally verified or “proven” if you will. Even time dilation has been experimentally verified
Isn't gamma calculated by both clock carriers (moving at a constant speed relative each other) the same? Suppose I have these readings of the clocks: t_s = 4 and t_m = 3 ... From the perspective of the moving clock (meaning, the moving clock considers itself stationary), they would make the analogous claim (I'm using primes): t'_s = 4 and t'_m = 3. So when we meet (and is this the crack?) we cannot agree (on the clock readings). Or: What elapsed time does the moving clock claim (what are they readings on their clock when I am claiming t_s=4 and t_m=3)? From my stationary perspective claiming t_m = 3; if I tell the passenger in the moving clock that their elapsed time is 3, would they agree that this is the reading on their clock? (I think they won't, they would claim it is 4). So, what is my problem?
You've come across the principle of relativity! Brian has (not yet) explicitly mentioned this. Lenny Susskind from Stanford University has demonstrated this in his old RUclips lectures. When you are in the system that is moving along with it, the observer who is, in reality, a stationary one, races past you with -v. And this observer in motion measures the same Lorenz factor for the stationary one. For that clocks have to be synchronized before. Example: Mu mesons, which race towards the Earth at almost the speed of light, "see" the Earth rush towards themselves and space in between contracts Lorentzian, which is why many more of them arrive on Earth undecayed. But keep in mind: moving clocks do tick slower! This prevents you from being taken in by the Twin Paradox. Greetings from Germany
Thanks for doing this. Me and my 2 daughters(11 and 8) are really enjoying these sessions. Some point please talk about the second law of thermodynamics.
Hello Brian: all human awareness lies within an envelope of one kind or another. Life-death, our solar system within our galaxy, and so on. My question to you is, "what lies beyond the beyond, what is our universe expanding into, what lies outside the envelope of the universe?"
Hi Prof Greene. Amazing video. I would like you to touch on the laws of thermodynamics in a video and go a little bit in to the concept of Entropy and how that ties back to how we deal with the concept of time. Thank you
Wish you would explain the gravitational time dilation effect. If time basically stops at the event horizon of a black hole from our perspective, I don't understand how they can effect the outside universe.
Hello Professor, thank you for this enlightening video. What I would like to see is the mathematical proof that time and space span a vector space and more precisely that they form a basis of the vector space, i.e. if a*x+b*y+c*z+d*t=0 where x,y,z are space coordinates, t is time and a,b,c,d are real numbers, then a=b=c=d=0
One question I've not had answered is: If frame of reference is symmetrical, why is time dilation asymmetrical? ie, you say 1 year passes for the high speed clock that leaves earth, when lifetimes may pass on earth, so why cant we make the same argument relative to the "high speed" clock? Relative to the travelling clock, the earth moves in the opposite direction at high speed, therefore time dilation works in the opposite sense, and 1 year on earth translates to lifetimes on the travelling clock. This appears on the surface to be a contradiction.
this is the basis of the 'twins paradox' the answer is that, if you always travel away at constant speed, both observers will see the other as being slowed down, like a bad zoom call: when you see the other person freeze, you know that you are only seeing an afterimage. It's the same principle: both observers see a ghostly projection of each other, moving slowly according to the gamma factor. But, deceleration 'fixes' this issue. If you return to EArth, you had to change velocity, and therefore your clock will be affected by this change in such a way that you can determine that it was in fact you who was moving, and no the Earth
@@hareecionelson5875 Thanks for the explanation. If the second observer caught up with the first observer instead of the first observer returning, would their clocks go back in sync?
@@morganga If the second observer did catch up to the moving observer, the second observer would have to accelerate, travel at a faster speed than the first, and then decelatre to the same speed as the first observer. During these acceleration periods, the second observer would see time pass quickly on the first observer's clock, like a quick burst of time, which would then slow down to the gamma factor when a constant velocity was reached.
Since we're playing around with relativity math... if the ratio of velocity to light-speed v/c is defined as sin(φ), where φ is the 'relativistic phase', then the Lorentz factor (gamma) is the secant of φ, i.e. γ = 1/√(1 - v²/c²) = 1/cos(φ). Intriguingly, this phase angle can be generalized to describe the curvature in a weak gravitational field, viz. sin²(φ) = 2GM/rc², since v is the escape velocity from radius r. Fun fact: relativistic phase (φ) goes to π/2 at the event horizon of a Schwarzschild black hole.
Excellent video Professor Greene! I look forward to the next instalment. I'd like to see the derivation of the E= mc² equation. I also want to see the equations of General Relativity, Maxwell's Eqns. Schrödinger's eqns, Dirac's equations. That's sufficient for a few weeks.......
Wonderful! Thanks so much mate. I'd absolutely love to look at some curved space-time stuff, though I understand completely that it's quite full on. Maybe the Friedman equations? Oh and the classical wave equation compared to the Schroedinger equation!!! Or just anything that you think is interesting, because you do a phenomenal job making everything engaging and exciting. Love your work Brian! Cheers
To say that less "tik toks" on the moving clock means that less time passed, is to asume that the number of "tik toks" somehow defines the passed quantity of time. But that doesnt mean that if you put two people next to the klocks, that the moving person aged less than the other one. It just means that the light clock next to him made less "tik toks". So to say that the number of "tik toks" on this aparatus has anything to say obout the true passage of time, would mean that time in this case is very poorly defined. Please correct me if I am wrong or if I am missing something. I would very much appreciate that. Because I really want to understand this! Thank you ^^
You also need to consider the principle of Relativity. Each observer can consider themselves at rest. And each one can say "this many tik Tom's correspond to this much aging of my body" and they will get the same number. They could both be at rest with each other or not, that doesn't change the number with respect to their own clock. That must mean that if we see fewer tik toks there is less aging.
"the number of "tik toks" on this aparatus has anything to say obout the true passage of time" In isolation you are correct, this feels like an issue with the light clock as opposed to the passage of actual time. Thought experiment: on Earth you feel like you are at rest. But you know you are moving through space. You are in a closed laboratory with a light clock and a mechanical clock. If the mechanical clock does not run slow, then you could compare the 'ticks' of the light clock to the ticks of your reliable watch. And, if you're a clever boy and remember the gamma factor equation, you could do the calculation and actually calculate your constant speed. But, that's not allowed: movement is always 'relative' to something, so how can you know your absolute speed through space? Therefore, either space IS absolute and we move according to a fixed coordinate grid of the universe. OR, your mechanical watch also runs slow by the exact same amount as the light clock, because the passage of time for you and everything moving (relative to another observer, of course), literally runs slower
Dear Greene, Thank you for making it so simple for a layman like me. I imagine the very photon as a spaceship. Then the photon defies time lapse on its original source (star) and the time it takes to reach us must have been slowed down. The effect should be that the photon from a star (say) ten light years away from us does not take so much time to reach us (due to time dilation). This is, of course, not taking into consideration of expanding universe. If this is true, I have so many questions to ask. -Illa Ravi, Vijyawada, Andhra Pradesh, India.
Am I correct in thinking that- in the animation of the light clocks, one being stationary and another one moving, it would be a better representation to show the clocks (recording the tik-tocs) separately and not sitting on top of the mirrors themselves? According to my understanding, the recording device sitting on top of the moving mirrors becomes a part of THAT system and hence should record the passage of time normally, not slowly. The slowing of the tic tocs will be recorded by an observer's clock at rest, relative to that moving clock system. Thank you in advance to anyone who can comment on this and correct me if I'm wrong. Brian- If you're reading this, thank you for everything you do!
Thank you Dr. Greene! I would love an explanation for the twin paradox! I wasn’t able to reason it out in my head. Wouldn’t the clock indeed be slower on the stationary object relative to the moving one? And if I went back wouldn’t each side respectively age slower relatively thereby cancelling it out?
You are correct: Both of you see a slow-motion ghost of the other, because both of you can claim to be 'at rest'. But, when you decelerate and change reference frames to get back to Earth, all that lagged time that you saw catches up in a quick burst during that deceleration period, like a film in fast forward, for just a few moments. If you never accelerated, indeed you would both see a slow motion ghost of the other, so it's quite sad because you'd both never see the present day versions of each other ever again. I would be watching in slow motion what you did last TUesday, and you'd be watching my last Tuesday too. :(
I believe another person commented regarding this question, but I too am curious. Hopefully I’m not too confused. The time dilation equation shows that to a stationary observer, (say on earth), a clock in motion, (on a rocket ship), should show a slightly slower time duration with respect to the duration for the stationary observer on earth. Conversely, for the observer in motion on the rocket ship, the time duration for the moving clock on the rocket ship should appear normal and the clock on earth should appear slower since for the moving observer, with no acceleration or direction changes, all objects around the observer should appear in motion and the rocket ship would appear stationary. With that argument, wouldn’t one expect people on earth to age less rapidly with respect to the time on the rocket ship?
This daily equation is just an awesome idea. Thanks Brian. If you run out of equations I might suggest you do different types of series. For example, a mini-series on famous (or not so well known might be even more interesting) thought experiments which of course is closely tied to equations would be nice. I personally wondered if it would be valid to think of space as being "eaten up" by large gravitational bodies instead of space only being stretched which is how it's always described which you thankfully touched on in your first episode (if I remember correctly) as I always had a problem visualizing a blackhole infinitely stretching space but if it's getting to "gobbled up" spacetime that infinity issue goes away. And now learning about dark energy it's like there's a counterpart where dark energy could be creating spacetime and blackholes destroying it making a nice balance of mechanisms for our universe... but I have never had a physicists or cosmologist friend to run this notion by so I've never had an feedback on whether such a way of looking these has any validity.
@@rohitdas475 me too awesome and beautiful explanation of time dilation and gamma factor. Can you explain something about the Einstein tensor and his field equations?
It is true that we cannot make absolute time clocks. Because when moving, speed affects force vectors interacting from the subatomic level. We should make a clock device that emits a laser beam in a direction perpendicular to the 2 mirrors (through a small hole). Place the sensor around 1/4 of the sphere with radius L from the laser emitter, opposite the direction of motion. Even creating a sensor sphere if you're worried about contraction of space. We will measure the theta deviation angle between the horizontal and diagonal directions of the light pulse ray. The frame of reference moves with a velocity V relative to a stationary point of O . Cos(theta)=v/c (theta is determined from Pi/2 to Pi and since cos(theta) is always v is always
Stuck in lockdown in New Zealand. This is perfect. Thank you so much for this. Going over these beautiful equations again is filling my heart and making my mind sing again as it has been awhile since I was reminded of their exquisiteness.
You should really consider showing the fundamental geometric derivation of gamma and Lorents factor. I discovered it was the most simple and universal shapes coming together in such a way that the exact figures came out nomatter what velocity you plug in. It could probably best be described as a simple complex geometric analysis of the riemann sphere.
For a straight section of railway line, try the world's longest; the 478 km stretch of the Indian-Pacific railway across the Nullabor Plain in southern Australia.
Thanks again Brian amazing lecture! Do you think you could talk about the equation for the Schwarzschild radius? I would love to learn more about black holes!
When I saw Pythagorean’s Theorem appear showing the relationship between time and space I had a religious experience. I am now one with the universe. 😌
I had this 'almost religious' moment in the first time I learned that a mathematical instrument invented thousands of years ago, was used to discover something so complex.
Cheers dig deeper
Irata, if you see this comment,
(1/gamma)^2 + (v/c)^2 = 1^2
not only is this a^2 + b^2 = c^2 (pythagoras)
this is x^2 + y^2 = 1, the unit circle. The big man. The circle of circles. also, the '1' has no units.
Pure 1 goodness, chilling with time dilation and the speed of light.
What you saw there was someone assume a theory to prove a theory. It was assumed that light can travel no faster or slower than c. It was also assumed that time is not universal so we get time dilation in addition to length contraction.
TD is a false concept! It is mathematically unworkable.
I'm a Mathematician and would love to see your take on some classical equations (Euler identity, Riemann zeta function and such). But if you intend to go on this Physics/Relativity path I suggest two topics:
1) Talking about surfaces, curvatures and a conversation about the Gauss-Bonnet formula (Relation between topology and geometry, genus and curvature);
2) Talking about the inverse square law and the way it manifests in various laws of physics (Gravitation, Electric potential and others).
This has been great, hope you do many more of those.
Your picture profile checks out.
I like the suggestion about the inverse square law. It's both powerful and strangely intuitive once you understand why it works.
Sir ,I have a doubt
Why is that ratio true.
∆ts/∆tm=L'/L
@@vijay_r_g He first used the famous equation for velocity
V=ΔS/Δt
Then he manipulated the equation to get
Δt = ΔS/V
And then he applied to our case. Note that in our case the velocity in both Δt and Δt' is C, the velocity of light, so when you make the ratio they end up cancelling each other.
I hope it was understandable. :)
Absolutely love these videos. Could listen to this all day. Brian Greene takes complicated ideas and makes them really easy to understand.
Yeah , for a dummy like me, this is very easy to understand
This explanation is just as clear as the summer sky ❤️
@@trnod Where do you live in the Netherlands? Lmao
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As somebody who doesn't know physics, I'm confused at if tm < ts, doesn't it also mean moving L is smaller than stationary L (since L=tc)? which means the moving world is smaller??
I know but thanks 😊
Hello Sir, thank you so much for making our time worth by such beautiful explanation. I am a Physics student from India. I would urge you to kindly make a video on the Einstein's Field Equations and GTR as a whole. Thank you so much.
Best explanation of time dilation ever!
The simplest and most unique explanation of time dilation I've ever seen... Thank you so much for creating for us this daily reminder of why physics is so beautiful and astonishing.
I thought I was fairly well versed in physics but I really don't see what speed has to do with time. In the example of two light clocks.
These are closed systems the speed of the light doesn't change and the distance between the mirrors don't change. From the clocks point of view nothing changes. One on Earth traveling at some set speed and the one on a ship traveling close to the speed of light. How does the clock care what's going on outside of it? It's a closed system and nothing in the system changes.!???
@@rayhaney7143 your perceived time doesn't change while you're moving but you and that clock are made of matter and energy which is effected by spacetime.
Motion is defined as the difference in the change of position that occured within some time interval. Classically speaking, you cannot move without changing position and you cannot change position without going through time.
The clock measures ticks and tocks while the speed of light cannot physically change. However, the velocity of the clock itself can change and if the ball of light stays in the clock as it moves then you can see that the ball of light would have a longer distance to travel from tick to tock. Since the speed of light remains constant there will be fewer ticks the faster the clock travels.
@@rayhaney7143 From each clock's point of view nothing is different since they are in non-accelerating frame of references. However, one observer looking at the other observer's clock will notice time dilation. The concept applies only to different frames of reference moving relative to each other.
I see my clock ticking right, you see your clock ticking right, but from my point of view your clock is ticking slower, because it is moving and light has to travel a longer way to reach the upper or the lower wall of your clock (the walls of your light clock are moving very fast away from the light wavefront).
@@larche Very interesting so of the clock was at Right angles to the motion would the light in this closed system miss the mirror entirely?
I mean if the speed of travel is effecting the clock at all
Brian is the only onle who helps me understand easy and quick.
Me too 😊
Amazing!! All equations are more beutiful when explained by you professor
The beauty of physics never ceases to amaze me
Me too
I want to take a moment Brian to thank you for the comfort these videos bring, lending a sense of normalcy through the stunning wonders of Mother Nature, to these crazy dangerous times we find ourselves in. For me you have ALWAYS done this, as I suffered through a lifelong illness of the mind. You and other great science communicators - such as your guests at World Science Festival discussions and others, brought me into the world of physics and science where my own difficulties were put in proper perspective against the backdrop of our majestic universe in all its glory and gob-smacking wonders. Then as now, here you are providing light in the darkness, amazing mysteries, theories and the power of empirical scientific method. In a world of fake news and trigger-pushing TV, how reassuring it is to have peer-reviewed and tested information, much from the shoulders of the giants that came before (Sagan, Einstein et al). How comforting you’ve been for me through the decades you’ve been reaching out with your great talent as scientist and communicator. Even now. My thanks have been too long coming, but while we’re all locked away in our homes or on the front lines of this battle, we can tune in to tried and tested truths to reassure and comfort us. Or just give us pause about what our priorities are, or even just to know that while Earth faces the biggest peacetime threat since 1919 we have so much to be amazed by and grateful for. No virus can Ever beat that. Thank you 👌👏🥰🎋🌿🦋🙌🏾
Maybe you can do the calculation how gravity affects time.
Its the same equation...
@@mikethek5494 No. you're stepping into general relativity vs special relativity. A lot more complex
It is the same equation in principle(pun intended)...think Einstein’s equivalence principle...gravity and acceleration are indistinguishable or ‘equivalent’...let’s not try to over complicate some seriously complicated shit🤪🤯🤔
I recommend the Heisenberg Uncertainty equation... Nice video!
Awesome, great idea to have this on every day, Excellent explanation Dr. Greene, How about how Gravity effects Time would be interesting !!
Agreed, also how it affects the speed of massless particles.
And we have teachers who derive the equation 3 pages long😭😭😭
Once again, Brian, with the current pandemic, how about an analysis of the general logistic equation? Particularly the differential form, but also the integral. It would be a very useful contribution to public understanding if done well, I think.
Love the concept behind this series, thanks.
Thank you again, sir. I remember an airplane experiment confirming this. I just looked it up and find it is the Hafale-Keating experiment (on Wikipedia), 1971. like the laser measurement of distance to the moon, it's nice to have experimental evidence demonstrate the irrefutably logical.
I would like to see a video on the Twin Paradox. One of the explanations I found says that the difference in age comes due the acceleration (General Relativity) that the twin on the rocket ship experiences when he turns around to come back to earth. This acceleration is not experienced by the twin on the earth. I'm not sure if this is the wright answer, or if an explanation for the paradox can be given completely within the realms of Special Relativity.
It’s three years later and this is the only comment I can see addressing the twins paradox.
Your explanation is completely correct, I think. The twin on the spaceship has to turn around and come home which involves acceleration and special relativity can’t deal with acceleration.
Dear Prof. Greene, thank you for an excellent explanation of the Gamma factor. I have recently started reading your new book - "Until the End of Time" - and I am thoroughly enjoying it. May I also express my gratitude for the "Quantum Leap" episode, in the Fabric of the Cosmos TV series. That is probably the best ever visualisation & explanation of the Schrodinger Wave function, that anyone can ever see.. Thanks again and please keep up the great work. Best wishes from Paul C., on lockdown in West Wales !!
Do you think he would read this???
I'm a 4th year undergrad in physics and I have never fully understood time dilation until this explanation. I've watched other videos on it and now I truly understand. Thank you
as a 4th year student, have you thought that it was suspicious that a v/c of 0.5 gives a gamma of 2/root3,
and a v/c of root3/2 gives as gamma of 2?
smells like... sine and cosine of 30 and 60 degrees, no?
Loved you explanation Prof Greene! The use of the Pythagorean theorem
was just beautiful. Thanks a lot!
there's another hidden pythagoras in the gamma equation; I recommend taking the inverse of gamma, 1/gamma= SqRt(1 - (v/c)^2).
Square both sides and add (v/c)^2 to both sides.
Another pythagoras.
These videos are wonderful. Thank you so much
Wonderful, thank you for taking up your time to so eloquently explain the beauty of maths and physics
Thank you Brian Greene
Sir, I great fan of yours, the way you explain the complicated things in simpler form is awesome.
I have request if you can present something on Nibru.
Awesome professor. That's the true elegance of physics. Unfortunately many physics lecturers miss this wonderful opportunity, as being seen in India. They just don't care about it's elegance, just memorizing everything. The Indian have ended up thinking Engineering is the best and nothing could exceed this, but it is just because they doesn't know about theoretical physics.
I was having some confusion regarding time dilation but now after going through last demonstration everything is clear in my mind........
Something just clicked! Thank you for the great content.
These videos are my recreation in every sense. Thanks so much.
Thank you Professor Brian Greene. You heard me. Thank you very much again. You're my Idol. I hope I can explain things like you did
I think the time dilation derivation can be simplified: The stationary observer measures time for horizontal distance of the moving light clock as vΔt, but he also measures the same time for diagonal distance L’ as
c Δt. As for the vertical distance L, it is measured by the moving observer as c Δt-moving. (I.e., the time he measures on the moving inertial frame for the up and down trajectory of the light). Applying the Pythagorean theorem the dilation relation follows between Δt and Δt-moving. So no need to assume L’/L = stationary time/moving time proportion before hand. Am I wrong professor? Thank you for all you do for the general public.
Super, Brian. Regarding the twin paradox time dilation not being applicable to the twin on earth: Is this due to the space bound twin's acceleration to close to the speed of light? What about the subsequent deceleration on the that twin's return to earth?
Brilliant presentation... I finally understood how time and space are related... It seems now so simple... Before it was like if I could not understand that the earth could not be anything than flat... Thank you.
Thank you for doing this Brian. I have watched many of your presentations but I like the added math here. It helps greatly to understand the ideas.
One of my favorite equations is the one for exponential growth and decay. I always was thought that it was awesome that one equation could be used to calculate compound interest and the growth rate of bacteria. I think it's also pertinent equation for our current situation.
Jenga Game would love to see that one as well.
I know this is three-years-old already but I just bumped into it and I loved it, my question is - of course - about time travel in this specific equation, so what you've established is the theoretically you can time travel in the future if you travel at or near the speed of light, what I also understand is it has been established that the universal speed limit IS indeed the speed of light, the question is that if by any way it is possible to exceed the speed of light, would time theoretically go backwards? Or maybe the speed of light is sort of the highway on which time travels so it doesn't matter YOUR speed just how fast you get from point a to point b on that highway?
Thank you sir Brian for all your videos and time you have dedicated to explain, us the normal people, how physics works. Greatly appreciate it!
Took and online course with Larry R. Langerstrom [Stanford Univ.] on Understanding Einstein's Special theory of Relativity. Had I not had this course, I'd not be ab;e follow Greene's math . It was done at a much slower pace than done here. Leading clocks lag!
Brian, you are the most brilliant science teacher that has ever lived! Perhaps you can help me with this question: Of course special relativity has been confirmed by several experiments.Could we also explain the results of these experiments with Lorentz theory of light, if only we choose to believe in a more complicated theory? Thanks!
thanks proffessor Greene you really made those theories interesting and simple to understand, it would be really amazing to watch your explaination on one of the best equations you have discovered during hunt for superstring theory.
Yes the elegance of the mathematical structure!
Thank you professor Greene!
Hi Brian! Kevin here. At 18:24, you said if we grew up in a world that had our daily activities at relativistic speeds, we would have better appreciated the effect speed has on time. However, I think that may not be totally true because we'd equally be used to that particular scale of time if we existed in a relativistic world. It may even be more difficult for us to appreciate Time dilation in such a scenario since we may have to be moving at slower speeds to observe how time moves faster for such cases; just because we may not be able to get any faster since we can't get faster than light. Just my thoughts, Prof. I hope you understand my suggestion
A wonderful clear and comprehensive explanation. Thank You.
Hi , i am not matematician , i am VFX and Cgi designer and this is so interesting to me , thanks for your lessons :-)
I have never found a better explanation to time dilation
Thank you Professor Greene for your explanation of a very difficult topic. I commented to ask what website has the clock differential demonstration. It's a powerful way to demonstrate the effect.
So exciting! 🤗🤗🤗
A fundamental yet little-known equation of special relativity is:
s4 = c3
where c3 is the speed of light through 3-dimensional space and s4 is the speed of anything (including light) through 4-dimensional spacetime, and furthermore it's a constant. The equation implies the following:
1. Light doesn't age (its speed through time is zero).
2. Anything that travels faster than c3 through 3-dimensional space must travel backward in time.
3. Assuming nothing can travel backward in time, nothing can travel faster than c3 through 3-dimensional space. (A famous inequality.)
4. The faster anything travels through 3-dimensional space, the slower it ages. (Also known as Time Dilation.)
I think s4=c3 should be taught in any course on special relativity. Although c3 is widely accepted as a "fundamental" constant, perhaps s4 is what's actually fundamental.
Thank you Brian it is wonderful how you make us feel belonging to the universe
Awesome explanation. Thank you. Question: How did scientists know in 1905 that speed of light is constant?
Your explanation of the phenomenon is so simple and beautiful! Thanks
Yeah, but he would never reply to this
profound truth explained so beautifully and simply! the use of Pythagoras theorem is a key point in this model, but what for Non Euclidean geometries? examples?
Dr Greene you are my Guru thank you for your work🎉
I have a very silly doubt Dr. Greene. I seem to understand it but when I think deeply I tend to get confused. So here's my doubt:-
Since the speed of light is constant and a larger distance needs to be covered in the moving clock from our perspective, then a larger time should elapse covering that larger distance in the moving clock compared to the stationary clock. That means time should elapse faster in moving clocks.
It would be very helpful if you could clear this silly doubt of mine. Thank you, Sir!
Thank you very much for your explanation. That's really clear and helpful.
Really helped visualize what was discussed in the elegant universe!
True
1- On the constance of the speed of light, is it a hypothesis, mathematical conclusion, experimental results or all combined ?
2- When deriving the equation, why assuming the space is Euclidean ?
Adama Diallo it’s all of them, the speed of light started as a theoretical anomaly but has been experimentally verified over and over again. It’s definitely far beyond a hypothesis, all of Einstein’s physics is based on the constant speed of light and it’s all experimentally verified or “proven” if you will. Even time dilation has been experimentally verified
Isn't gamma calculated by both clock carriers (moving at a constant speed relative each other) the same? Suppose I have these readings of the clocks: t_s = 4 and t_m = 3 ... From the perspective of the moving clock (meaning, the moving clock considers itself stationary), they would make the analogous claim (I'm using primes): t'_s = 4 and t'_m = 3. So when we meet (and is this the crack?) we cannot agree (on the clock readings).
Or: What elapsed time does the moving clock claim (what are they readings on their clock when I am claiming t_s=4 and t_m=3)? From my stationary perspective claiming t_m = 3; if I tell the passenger in the moving clock that their elapsed time is 3, would they agree that this is the reading on their clock? (I think they won't, they would claim it is 4).
So, what is my problem?
You've come across the principle of relativity! Brian has (not yet) explicitly mentioned this. Lenny Susskind from Stanford University has demonstrated this in his old RUclips lectures. When you are in the system that is moving along with it, the observer who is, in reality, a stationary one, races past you with -v. And this observer in motion measures the same Lorenz factor for the stationary one. For that clocks have to be synchronized before. Example: Mu mesons, which race towards the Earth at almost the speed of light, "see" the Earth rush towards themselves and space in between contracts Lorentzian, which is why many more of them arrive on Earth undecayed. But keep in mind: moving clocks do tick slower!
This prevents you from being taken in by the Twin Paradox.
Greetings from Germany
Love the "light clock". And -for a more distant future - what is spinor, tensor, Hopf fibration, Penrose's CCC hypothesis, etc... Many thanks
excellent explanation to a complex concept.!
Brian i would love to see the explanation of the extended version of E=mc2 with momentum and its implications. Thank you for the vídeos!
Thanks for doing this. Me and my 2 daughters(11 and 8) are really enjoying these sessions. Some point please talk about the second law of thermodynamics.
Hello Brian: all human awareness lies within an envelope of one kind or another. Life-death, our solar system within our galaxy, and so on. My question to you is, "what lies beyond the beyond, what is our universe expanding into, what lies outside the envelope of the universe?"
Hi Prof Greene.
Amazing video. I would like you to touch on the laws of thermodynamics in a video and go a little bit in to the concept of Entropy and how that ties back to how we deal with the concept of time. Thank you
Wish you would explain the gravitational time dilation effect. If time basically stops at the event horizon of a black hole from our perspective, I don't understand how they can effect the outside universe.
Hello Professor, thank you for this enlightening video. What I would like to see is the mathematical proof that time and space span a vector space and more precisely that they form a basis of the vector space, i.e. if a*x+b*y+c*z+d*t=0 where x,y,z are space coordinates, t is time and a,b,c,d are real numbers, then a=b=c=d=0
Please made a video on quantum gravity prof. Greene
Very well done. Adding another vote for the Dirac equation!
Brian Greene.....
Greatest name in Physics...
Thanks for having such an amazing demonstration
One question I've not had answered is: If frame of reference is symmetrical, why is time dilation asymmetrical? ie, you say 1 year passes for the high speed clock that leaves earth, when lifetimes may pass on earth, so why cant we make the same argument relative to the "high speed" clock? Relative to the travelling clock, the earth moves in the opposite direction at high speed, therefore time dilation works in the opposite sense, and 1 year on earth translates to lifetimes on the travelling clock. This appears on the surface to be a contradiction.
this is the basis of the 'twins paradox'
the answer is that, if you always travel away at constant speed, both observers will see the other as being slowed down, like a bad zoom call: when you see the other person freeze, you know that you are only seeing an afterimage. It's the same principle: both observers see a ghostly projection of each other, moving slowly according to the gamma factor.
But, deceleration 'fixes' this issue. If you return to EArth, you had to change velocity, and therefore your clock will be affected by this change in such a way that you can determine that it was in fact you who was moving, and no the Earth
@@hareecionelson5875 Thanks for the explanation. If the second observer caught up with the first observer instead of the first observer returning, would their clocks go back in sync?
@@morganga If the second observer did catch up to the moving observer, the second observer would have to accelerate, travel at a faster speed than the first, and then decelatre to the same speed as the first observer.
During these acceleration periods, the second observer would see time pass quickly on the first observer's clock, like a quick burst of time, which would then slow down to the gamma factor when a constant velocity was reached.
Since we're playing around with relativity math... if the ratio of velocity to light-speed v/c is defined as sin(φ), where φ is the 'relativistic phase', then the Lorentz factor (gamma) is the secant of φ, i.e. γ = 1/√(1 - v²/c²) = 1/cos(φ). Intriguingly, this phase angle can be generalized to describe the curvature in a weak gravitational field, viz. sin²(φ) = 2GM/rc², since v is the escape velocity from radius r. Fun fact: relativistic phase (φ) goes to π/2 at the event horizon of a Schwarzschild black hole.
Thank you Brian. I am learning so much. Joan from Manchester, England.
Don't give info about your self
So many thanks dear professor for your nice explanation
Excellent video Professor Greene! I look forward to the next instalment. I'd like to see the derivation of the E= mc² equation. I also want to see the equations of General Relativity, Maxwell's Eqns. Schrödinger's eqns, Dirac's equations. That's sufficient for a few weeks.......
Please do the formula for gravitational force
Wonderful! Thanks so much mate. I'd absolutely love to look at some curved space-time stuff, though I understand completely that it's quite full on. Maybe the Friedman equations? Oh and the classical wave equation compared to the Schroedinger equation!!! Or just anything that you think is interesting, because you do a phenomenal job making everything engaging and exciting. Love your work Brian! Cheers
You are correct sir. It was Albert Einstein that made the light clock.
Thank you so much for your videos!!!!
Amazing to have such a demonstration...
I understood it perfectly. Thank u😊
To say that less "tik toks" on the moving clock means that less time passed, is to asume that the number of "tik toks" somehow defines the passed quantity of time. But that doesnt mean that if you put two people next to the klocks, that the moving person aged less than the other one. It just means that the light clock next to him made less "tik toks".
So to say that the number of "tik toks" on this aparatus has anything to say obout the true passage of time, would mean that time in this case is very poorly defined.
Please correct me if I am wrong or if I am missing something. I would very much appreciate that. Because I really want to understand this! Thank you ^^
You also need to consider the principle of Relativity. Each observer can consider themselves at rest.
And each one can say "this many tik Tom's correspond to this much aging of my body" and they will get the same number. They could both be at rest with each other or not, that doesn't change the number with respect to their own clock.
That must mean that if we see fewer tik toks there is less aging.
"the number of "tik toks" on this aparatus has anything to say obout the true passage of time"
In isolation you are correct, this feels like an issue with the light clock as opposed to the passage of actual time.
Thought experiment: on Earth you feel like you are at rest. But you know you are moving through space. You are in a closed laboratory with a light clock and a mechanical clock.
If the mechanical clock does not run slow, then you could compare the 'ticks' of the light clock to the ticks of your reliable watch.
And, if you're a clever boy and remember the gamma factor equation, you could do the calculation and actually calculate your constant speed. But, that's not allowed: movement is always 'relative' to something, so how can you know your absolute speed through space?
Therefore, either space IS absolute and we move according to a fixed coordinate grid of the universe. OR, your mechanical watch also runs slow by the exact same amount as the light clock, because the passage of time for you and everything moving (relative to another observer, of course), literally runs slower
Dear Greene, Thank you for making it so simple for a layman like me. I imagine the very photon as a spaceship. Then the photon defies time lapse on its original source (star) and the time it takes to reach us must have been slowed down. The effect should be that the photon from a star (say) ten light years away from us does not take so much time to reach us (due to time dilation). This is, of course, not taking into consideration of expanding universe. If this is true, I have so many questions to ask.
-Illa Ravi, Vijyawada, Andhra Pradesh, India.
Am I correct in thinking that- in the animation of the light clocks, one being stationary and another one moving, it would be a better representation to show the clocks (recording the tik-tocs) separately and not sitting on top of the mirrors themselves? According to my understanding, the recording device sitting on top of the moving mirrors becomes a part of THAT system and hence should record the passage of time normally, not slowly. The slowing of the tic tocs will be recorded by an observer's clock at rest, relative to that moving clock system. Thank you in advance to anyone who can comment on this and correct me if I'm wrong. Brian- If you're reading this, thank you for everything you do!
im currently a freshman studying physics and god damnit you are such a great teacher and narrator please keep up the good work:)
He's actually a pretty well-known theoretical physicist, this might be the reason he's so good.
Thank you Dr. Greene! I would love an explanation for the twin paradox! I wasn’t able to reason it out in my head.
Wouldn’t the clock indeed be slower on the stationary object relative to the moving one? And if I went back wouldn’t each side respectively age slower relatively thereby cancelling it out?
You are correct: Both of you see a slow-motion ghost of the other, because both of you can claim to be 'at rest'.
But, when you decelerate and change reference frames to get back to Earth, all that lagged time that you saw catches up in a quick burst during that deceleration period, like a film in fast forward, for just a few moments.
If you never accelerated, indeed you would both see a slow motion ghost of the other, so it's quite sad because you'd both never see the present day versions of each other ever again. I would be watching in slow motion what you did last TUesday, and you'd be watching my last Tuesday too. :(
I believe another person commented regarding this question, but I too am curious. Hopefully I’m not too confused. The time dilation equation shows that to a stationary observer, (say on earth), a clock in motion, (on a rocket ship), should show a slightly slower time duration with respect to the duration for the stationary observer on earth. Conversely, for the observer in motion on the rocket ship, the time duration for the moving clock on the rocket ship should appear normal and the clock on earth should appear slower since for the moving observer, with no acceleration or direction changes, all objects around the observer should appear in motion and the rocket ship would appear stationary. With that argument, wouldn’t one expect people on earth to age less rapidly with respect to the time on the rocket ship?
This daily equation is just an awesome idea. Thanks Brian. If you run out of equations I might suggest you do different types of series. For example, a mini-series on famous (or not so well known might be even more interesting) thought experiments which of course is closely tied to equations would be nice.
I personally wondered if it would be valid to think of space as being "eaten up" by large gravitational bodies instead of space only being stretched which is how it's always described which you thankfully touched on in your first episode (if I remember correctly) as I always had a problem visualizing a blackhole infinitely stretching space but if it's getting to "gobbled up" spacetime that infinity issue goes away. And now learning about dark energy it's like there's a counterpart where dark energy could be creating spacetime and blackholes destroying it making a nice balance of mechanisms for our universe... but I have never had a physicists or cosmologist friend to run this notion by so I've never had an feedback on whether such a way of looking these has any validity.
Do you think he would ever read this " paragraph "
Excellent and thank for dealing later with the twin paradox
Very helpful sir..While Listening to you and understanding physics and mathematics seems so easy and interesting.. Thanks from India.. 😊✌️👍
WoW! I'm so happy to have discovered this...once more, all my gratitude!
Do the dark energy and dark matter equation please
Definitely---we will surely cover some cosmology.
@@briangreene407 YES!!
Kudos ..i also want that Brian
@@rohitdas475 me too awesome and beautiful explanation of time dilation and gamma factor. Can you explain something about the Einstein tensor and his field equations?
It is true that we cannot make absolute time clocks.
Because when moving, speed affects force vectors interacting from the subatomic level.
We should make a clock device that emits a laser beam in a direction perpendicular to the 2 mirrors (through a small hole). Place the sensor around 1/4 of the sphere with radius L from the laser emitter, opposite the direction of motion. Even creating a sensor sphere if you're worried about contraction of space.
We will measure the theta deviation angle between the horizontal and diagonal directions of the light pulse ray.
The frame of reference moves with a velocity V relative to a stationary point of O .
Cos(theta)=v/c (theta is determined from Pi/2 to Pi and since cos(theta) is always v is always
Thanks for sharing your time & knowledge, Brian
Yeah, he is a busy man. He does calculations all day
Stuck in lockdown in New Zealand. This is perfect. Thank you so much for this. Going over these beautiful equations again is filling my heart and making my mind sing again as it has been awhile since I was reminded of their exquisiteness.
You should really consider showing the fundamental geometric derivation of gamma and Lorents factor.
I discovered it was the most simple and universal shapes coming together in such a way that the exact figures came out nomatter what velocity you plug in. It could probably best be described as a simple complex geometric analysis of the riemann sphere.
I can’t wait for Brian’s next book!!
For a straight section of railway line, try the world's longest; the 478 km stretch of the Indian-Pacific railway across the Nullabor Plain in southern Australia.
Thanks again Brian amazing lecture! Do you think you could talk about the equation for the Schwarzschild radius? I would love to learn more about black holes!