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. :)
Thanks brian greene my head hurt a little while trying to understand your equation but i was able to somehow. I was not thinking that the whole equation is drawn from the our perspective/Observers perspective. Its sad the equation is meaningless with v=c(I dont know what does this even mean, Does it implies that time is infinite => so space/universe is infinite) and v>c(i.e can't go back in time), Nice assumption anyway
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?
Tic-Tock, it is two. At every two movements, it goes back to the starting point. Binal counting. How about adding one more to make it to three, say, Tic- Tuck - Tock. Let's have a triangle of aligned mirror surrounding the ball of light go through the triangle and come back to the starting point. Let's see how this can explain the world in a different way.
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
Please explain why flipping the argument around around doesn't work? From the point of view of the astronaut he might say that the earth is travelling away from him and so earth's clocks would be running slow...
After you do einsteins field equations, I would appreciate it if you showed us the equation that shows the motion and behavior of a gravitational wave. I'm working on a paper that could potentially unify the four fundamental forces and I need this equation.
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.
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.
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.
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.......
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´m not a mathematician and would love to have some words and maybe a small equation about the "loaf of space" and how it works. I find it extremely interesting but difficult to fully understand.
Im an amateur physicist, my minds eye doesnt picture things well, so keeping track of numbers and equations in my brain is uber hard to do from memory haha. Also i was never able to pursue it academically because of financial reasons, as is the reason for many, and so i dont even know what Delta means or is specifically used for along with other symbols. Little explanations would be greatly appreciated xD So i dont remember nearly any specific equations or even why i would want to suggest to talk about them and so any equation you teach us about is alright with me! Also, my only physics book i own is Issac Asimov Understanding Physics: All 3 volumes in one. Now while i understand we have come a long way since the 60's, and things like the Aether have been debunked in a way, i wanted to ask, and fellow commenters feel free to help out, is it a good book to get the basics of understanding these patterns and ultimately the equations, or is a lot of it too out of date to make any use of nowadays? I read about to the last volume, then the book fell apart, literally, and so i havent picked it back up but recently ive been wanting to go through it and write down all the equations in it, for memories sake haha
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?
Dear Sir, it would be really helpful if you could spend a video discussing the Euler-Lagrange equation, and how it can be derived using simple physical arguments rather than simply doing math. Please also explain the physical meaning of Lagrangian. One question I'd like to ask is that what shall be the course of study of a physics undergraduate looking forward to a career in theoretical physics?
The physical meaning of Lagrangian? What an excellent question. It makes one wonder if there is a physical meaning for every mathematical object. I think I have found the physical meaning of i square equals -1. which is the unit oscillation of polarity, i. e. the prohibition of squaring the same polarity. This is the case of a particle that is identical to its anti-particle. If Brian could only produce a similar explanation for Lagrangian, eh.
I believe the difference between kinetic energy and potential energy , which we call the Lagrangian, must have a physical meaning related to it and is not merely a mathematical construct. I find it quite remarkable that such a quantity can give all we need to know about a system.
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 !!
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
Thank you Professor, i would like to ask a question: if we try to imagine the moving Clock at speed of light is at rest relative to the stationary clock, and in the fixed direction ; the stationary clock slow experiences time differently and slower! ? I am look forward to get my answer sir. I would like to suggest in further episodes, please explain the lemaitre math and start of Big bang. Thanks
may I ask a question: let say you move around the the radio station close the to the speed of light. you speak truth the radio and because you move around the station the distance of radio wave is fixed what we will listen from the radio is your talking will be solwer or the same or maybe i didn't understood the talk :( thanks in advance
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??
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🤪🤯🤔
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.
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.
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.
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.
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!
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.
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.
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!
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?
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
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
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).
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.
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.
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.
No matter how many times I look at this I am still totally at a loss. The premise that *any type* of clock slows down when moving is absurd to me. The way I see it is that the gamma factor is derived (for want of a better word) because the "model" uses light to measure distance and in my mind that is the "issue" in my mind. The light going up and down in a stationary light clock takes 2L/C (I agree with that) and the light going the diagonal route in the moving light-clock takes 2H/C where H, the hypotenuse and takes sqrt(L^2+(V*t)^2)/C (where V is the velocity of the train). So I understand the geometry (Pythagoras) and can see how the travelling light-clock slows down (there is a physical reason) but I can't see how that translates to a battery operated digital clock observed by either the traveller or a stationary observer. So, I suppose my question boils down to "How does one demonstrate the effect of "Time dilation" on a battery operated clock - what physical "phenomena" is taking place?"
u are right. The clock mechanism does not depend on the (relative) speed except for ...one type of clock, atomic ones that can be an ideal isolated system. This "light clock" is only a thought clock in order to explain the equation of Lorentz but physically it refers only to a system clock (it must be an ideal closed system of a field)now available: only atomic clock (the frequency of a wave depends on the potential gravitation and in theory on Relativistic Doppler effect but in practice, only on the first one like GPS-es (though in the calculation this component equals the effect of inertial movement in a circle (like around the Earth)- usually it is not showed in textbooks except by R.Schlegel. The term "time dilation" has a sense if properly understood; it is a measurement problem and nothing about some dynamic changes in the mechanism of a moving clock or an observer!
@@krzysztofciuba271 Thanks for your reply. Unfortunately, I am none the wiser. The "Twins problem" suggests that the *astronaut* twin returns to Earth to find the *sedentary* twin is older - implying that there is a physical (biological) aging difference?
@@MontyVideo969 ? u repeat a typical textbooks' interpretation; anyone (who has passed a mathematics exam) see that Lorentz's formulas are symmetric one: just switching an apostrophe of any parameter (x,y,z,t) and (x',y',z',t') plus just a sign of velocity, from + to '-"-all these means it is just mathematical (or kinematical) transformation. Make a Minkoviskian diagram from the point view of a "traveler" that would be at rest - what is his "proper" time and the other now traveling? A simple question that textbooks writers cannot answer!!! (All experiments only confirm the prediction from the point of view at rest the live time of "sub-particles"(rather quanta of a field) traveling in a cyclotron close to the speed of light or with the atomic clock in Earth's orbits influenced by the change of gravitational potential
This is a dumb question but do we know for sure that classical physics motion is solved completely by this equation as well as Einstein's general theory once he included mass and gravity as variables? That is to say, civilization thought Newton had the final, explain everything, equations for motion until Maxwell, Lorentz, and then Einstein came along. Are our only unsolved mysteries now in the quantum realm?
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
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!
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?
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
Maybe this question has already been raised (or is an innocent one...) but...according to quantum entanglement, speeds faster than C could be achieved; thus, the equation as is would force us to extract a square root of a negative number, which is a mathematical error/impossibility. Is there any other mathematical way to calculate time dilation in order to avoid geometry principles that prevent the considerations of faster than C speeds ? And, if possible, time dilation would result in a negative outcome...as if time would be "rolling back"...? Any take about this? Thank you Brian Greene ! This channel is amazing !
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.
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.
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
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. :)
Hi, awesome video! Has someone sat down to calculate how many years will have passed if you travel with the speed of light for one hour?
Thanks brian greene my head hurt a little while trying to understand your equation but i was able to somehow. I was not thinking that the whole equation is drawn from the our perspective/Observers perspective.
Its sad the equation is meaningless with v=c(I dont know what does this even mean, Does it implies that time is infinite => so space/universe is infinite) and v>c(i.e can't go back in time), Nice assumption anyway
Waiting for part three
Waiting dor part three
But why does time move slow for a fast moving observer?🤔
If we have a speed v=c than the gamma factor would be infinite.
So what does the infinity mean in this context?
I'm sorry, Professor, but you don't look well.
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?
Tic-Tock, it is two. At every two movements, it goes back to the starting point. Binal counting. How about adding one more to make it to three, say, Tic- Tuck - Tock. Let's have a triangle of aligned mirror surrounding the ball of light go through the triangle and come back to the starting point. Let's see how this can explain the world in a different way.
please make a video on Newton's law of Cooling
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
Brian, get softer lighting :) loving these episodes
Could you talk about Bootstrap paradox?
Please explain why flipping the argument around around doesn't work? From the point of view of the astronaut he might say that the earth is travelling away from him and so earth's clocks would be running slow...
I'm already addicted. Where is today's equation? (03/28)
After you do einsteins field equations, I would appreciate it if you showed us the equation that shows the motion and behavior of a gravitational wave. I'm working on a paper that could potentially unify the four fundamental forces and I need this equation.
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.
So time will stop if every motion in universe stop?
Or time will still elapse
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.
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.
Thank You Professor. These videos are absolute gem
For me, this is applicable 😊
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.......
Very well done. Adding another vote for the Dirac equation!
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'd like to see your approach to some thermodynamics, for example: ΔS
(univ
) = Δ
S
(sys
) + Δ
S
(surr
) ≥0
would really enjoy hearing a discussion of the Dirac equation.
Thanks Sir, You are owesome
I´m not a mathematician and would love to have some words and maybe a small equation about the "loaf of space" and how it works. I find it extremely interesting but difficult to fully understand.
Im an amateur physicist, my minds eye doesnt picture things well, so keeping track of numbers and equations in my brain is uber hard to do from memory haha. Also i was never able to pursue it academically because of financial reasons, as is the reason for many, and so i dont even know what Delta means or is specifically used for along with other symbols. Little explanations would be greatly appreciated xD So i dont remember nearly any specific equations or even why i would want to suggest to talk about them and so any equation you teach us about is alright with me! Also, my only physics book i own is Issac Asimov Understanding Physics: All 3 volumes in one. Now while i understand we have come a long way since the 60's, and things like the Aether have been debunked in a way, i wanted to ask, and fellow commenters feel free to help out, is it a good book to get the basics of understanding these patterns and ultimately the equations, or is a lot of it too out of date to make any use of nowadays? I read about to the last volume, then the book fell apart, literally, and so i havent picked it back up but recently ive been wanting to go through it and write down all the equations in it, for memories sake haha
Great and easy to understand
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.
Wonderful, thank you for taking up your time to so eloquently explain the beauty of maths and physics
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?
Dear Sir, it would be really helpful if you could spend a video discussing the Euler-Lagrange equation, and how it can be derived using simple physical arguments rather than simply doing math. Please also explain the physical meaning of Lagrangian.
One question I'd like to ask is that what shall be the course of study of a physics undergraduate looking forward to a career in theoretical physics?
The physical meaning of Lagrangian? What an excellent question. It makes one wonder if there is a physical meaning for every mathematical object. I think I have found the physical meaning of i square equals -1. which is the unit oscillation of polarity, i. e. the prohibition of squaring the same polarity. This is the case of a particle that is identical to its anti-particle. If Brian could only produce a similar explanation for Lagrangian, eh.
I believe the difference between kinetic energy and potential energy , which we call the Lagrangian, must have a physical meaning related to it and is not merely a mathematical construct. I find it quite remarkable that such a quantity can give all we need to know about a system.
This explanation is just as clear as the summer sky ❤️
@@trnod Where do you live in the Netherlands? Lmao
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Ki
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Maxwell's 4th Equation , Sir
Thank you prof Green, what a great idea!
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???
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!
How about looking at Boltzmann equation? It looks simple but like Einstein’s equation is so profound.
Dirac equation please, thankyou for your daily equations. Stay safe.
How did max Planck Derive the Plank scale? Carl
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
Really great series. Thanks!
Loved it!
I’m loving your videos. So is this time elongation formula used in the GPS navigation satellites algorithms? I assume so.
Thank you Professor, i would like to ask a question: if we try to imagine the moving Clock at speed of light is at rest relative to the stationary clock, and in the fixed direction ; the stationary clock slow experiences time differently and slower! ?
I am look forward to get my answer sir.
I would like to suggest in further episodes, please explain the lemaitre math and start of Big bang.
Thanks
may I ask a question:
let say you move around the the radio station close the to the speed of light.
you speak truth the radio and
because you move around the station the distance of radio wave is fixed
what we will listen from the radio is your talking will be solwer or the same
or maybe i didn't understood the talk :(
thanks in advance
See the Doppler effect. When a siren (in an ambulance) passes you , u hear the frequency drop.
Brian Greene.....
Greatest name in Physics...
Sir,how about Maxwell's eqation which United electricity n magnetism
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 😊
Brian is the only onle who helps me understand easy and quick.
Me too 😊
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🤪🤯🤔
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 beauty of physics never ceases to amaze me
Me too
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.
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.
Amazing!! All equations are more beutiful when explained by you professor
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.
Thank you Brian Greene
Best explanation of time dilation ever!
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.
Something just clicked! Thank you for the great content.
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!
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
These videos are wonderful. Thank you so much
And we have teachers who derive the equation 3 pages long😭😭😭
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.
I was having some confusion regarding time dilation but now after going through last demonstration everything is clear in my mind........
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.
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!
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 professor Greene!
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
So exciting! 🤗🤗🤗
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
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
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.
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.
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.
Your explanation of the phenomenon is so simple and beautiful! Thanks
Yeah, but he would never reply to this
Awesome explanation. Thank you. Question: How did scientists know in 1905 that speed of light is constant?
No matter how many times I look at this I am still totally at a loss. The premise that *any type* of clock slows down when moving is absurd to me. The way I see it is that the gamma factor is derived (for want of a better word) because the "model" uses light to measure distance and in my mind that is the "issue" in my mind. The light going up and down in a stationary light clock takes 2L/C (I agree with that) and the light going the diagonal route in the moving light-clock takes 2H/C where H, the hypotenuse and takes sqrt(L^2+(V*t)^2)/C (where V is the velocity of the train). So I understand the geometry (Pythagoras) and can see how the travelling light-clock slows down (there is a physical reason) but I can't see how that translates to a battery operated digital clock observed by either the traveller or a stationary observer. So, I suppose my question boils down to "How does one demonstrate the effect of "Time dilation" on a battery operated clock - what physical "phenomena" is taking place?"
u are right. The clock mechanism does not depend on the (relative) speed except for ...one type of clock, atomic ones that can be an ideal isolated system. This "light clock" is only a thought clock in order to explain the equation of Lorentz but physically it refers only to a system clock (it must be an ideal closed system of a field)now available: only atomic clock (the frequency of a wave depends on the potential gravitation and in theory on Relativistic Doppler effect but in practice, only on the first one like GPS-es (though in the calculation this component equals the effect of inertial movement in a circle (like around the Earth)- usually it is not showed in textbooks except by R.Schlegel. The term "time dilation" has a sense if properly understood; it is a measurement problem and nothing about some dynamic changes in the mechanism of a moving clock or an observer!
@@krzysztofciuba271 Thanks for your reply. Unfortunately, I am none the wiser. The "Twins problem" suggests that the *astronaut* twin returns to Earth to find the *sedentary* twin is older - implying that there is a physical (biological) aging difference?
@@MontyVideo969 ? u repeat a typical textbooks' interpretation; anyone (who has passed a mathematics exam) see that Lorentz's formulas are symmetric one: just switching an apostrophe of any parameter (x,y,z,t) and (x',y',z',t') plus just a sign of velocity, from + to '-"-all these means it is just mathematical (or kinematical) transformation. Make a Minkoviskian diagram from the point view of a "traveler" that would be at rest - what is his "proper" time and the other now traveling? A simple question that textbooks writers cannot answer!!! (All experiments only confirm the prediction from the point of view at rest the live time of "sub-particles"(rather quanta of a field) traveling in a cyclotron close to the speed of light or with the atomic clock in Earth's orbits influenced by the change of gravitational potential
@@krzysztofciuba271 Thanks. I still don't comprehend time dilation. Perhaps I'm too Newtonian lol.
I know this is late but you have to understand the fact that light is the speed of causality. It's the speed in which reality happens.
Dr Greene you are my Guru thank you for your work🎉
This is a dumb question but do we know for sure that classical physics motion is solved completely by this equation as well as Einstein's general theory once he included mass and gravity as variables? That is to say, civilization thought Newton had the final, explain everything, equations for motion until Maxwell, Lorentz, and then Einstein came along. Are our only unsolved mysteries now in the quantum realm?
The opposite is true: we're pretty sure that Einstein's relativity isn't quite right, as it's inconsistent with quantum mechanics.
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
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!
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. :(
excellent explanation to a complex concept.!
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?
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.
Maybe this question has already been raised (or is an innocent one...) but...according to quantum entanglement, speeds faster than C could be achieved; thus, the equation as is would force us to extract a square root of a negative number, which is a mathematical error/impossibility. Is there any other mathematical way to calculate time dilation in order to avoid geometry principles that prevent the considerations of faster than C speeds ? And, if possible, time dilation would result in a negative outcome...as if time would be "rolling back"...? Any take about this? Thank you Brian Greene ! This channel is amazing !
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.