Your Daily Equation #7: Relativistic Velocity Combination
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- čas přidán 5. 04. 2020
- Episode 07 #YourDailyEquation: If you race toward a beam of light, why doesn't the light approach you faster than the speed of light? If you race away from it, why doesn't the light approach you slower than the speed of light? In today's Daily Equation, Brian Greene describes the relativistic velocity combination law to provide an answer.
Even if your math is a bit rusty, join Brian Greene for brief and breezy discussions of pivotal equations and exciting stories of nature and numbers that will allow you to see the universe in a new way.
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Wow -- I have never seen these formulas (a 77+ old engineer with a passion for physics) -- you have really made my day in the lockdown for Covid-19 main candidates... ;-))
Loving Until the End of Time. , this was an absolute gem to watch
Thank you Brian. The relativistic velocity combination really made me sit up and take notice. I just love that you are taking the ti me to do this at this difficult time in everybody's life. You are a true champion.
A beautiful equation lucidly explained. The constancy of the speed of light is no longer counterintuitive
Well Dr Green, lots of people are hoping you will derive the speed of light being constant. Maybe through Maxwell's equations? That's the way I show it to my physics students. I don't know the easiest way to do it for this audience. But maybe, if you keep these going a little while, people could actually see where that comes from. I think it would be a worthwhile quest!
Brian you are my hero
Smooth as always Professor Greene!! I really appreciate it! ... So far has been an excellent experience!
This is so helpful learning like this! With this I can skip back if I miss something. In school it always feels so rushed. Thanks for these videos. I'm a big fan 🙏🏻
This is freaking awesome. I am enjoying this series so much! Thank you.
Excellent. I love these sessions with Dr. Greene.
These are fantastic and will provide a tremendous resource.
Yeah I always wondered about that. Elegant, beautiful and indeed rather simple. Thank you!
thank you so much for these videos, i've always loved your enthusiasm and way of explaining things! you're one of my favorite science educators, love your books too 💖🌌✌️
Really great episode! Each episode surprises me with how interesting it is!
Love you, Brian
Thank you Dr. Greene!!
I love these daily equations so much. Thanks for taking me back to my roots proffesor
excellent!! ~ i love that i can watch these over
Good to see you again 😊
I am so happy that he emphasized the fact that the equation with the correction factor is true for all speeds even with the very low speeds of Gracie and the egg. it is the ONLY correct way to add speeds. Many times I have had students ask me when the relativistic addition equation kicks in, and my answer was "at every speed, it is ALWAYS used."
Soo cool! thank you!
Brilliant, thanks alot
like the simplicity of your explanations. would you cover Einstein field equations?
I’m lovin it!!!
Priceless
I'll never forget when this finally clicked in my brain. It was my senior year in high school and I was sitting in physics not paying attention to the kinematics lesson that day haha. Right class, wrong lesson. I got so excited that it finally made sense...my teacher was less enthused lol
Yes and you tell this your secondary school teacher in physics and he tells you...
What the hell are you talking? 😂😂😂😂
I can relate to this, it actually happened to me haha. Not that he didn't believe me, just that it was beyond the physics he was actually there to teach.
@@jamestrexler6329 same thing happened to me today
Thanks!
I put the calculation from 12:48 min on Wolfram Alpha, " 2/(1-10^-16)", returned this value "2.00000000000000020000000000000002000...", yes, greater than 2.
❤️✌️
Thank you.
Hello, Professor Brian.
Thank you for sharing with us so much valuable information.
My suggestion is for an episode that tells the story of Newton's discovery of the gravitation’s law (and also the invention of calculus), exactly when he left London in the late seventeenth century to escape the plague.
Sergio Righini, São Paulo, Brazil.
Dear Prof. Greene,
how about:
let v=xc, w=yc => (v+w)/(1+vw/c^2) = c(x+y)/(1+xy)
let 0 ≤ x ≤ 1 and y ≤ 1 then x(1-y) ≤ 1-y or x+y ≤ 1+xy
=> c(x+y)/(1+xy) ≤ c
Also applies to negativ y: -1 ≤ y ≤ 0, |y| ≤ x your 2nd case.
BTW, the case x=1, y= -1 is only defined as a limit.
Very cool.
amazing thanks you
This equation also implies that light ignores time in it's own frame of reference. We can restate this by saying that the moment of emission and the moment of absorption for an emitted photon are IDENTICAL in it's reference frame. This raises some rather strange consequences. For one thing we can say that from the frame of reference of the photon, the photon does not exist at all. We can also say that the distance (no matter how far) between emission and absorption is zero which implies that in some sense, an energy transfer is taking place which takes zero time over zero distance (in the photonic reference frame). I'm not disputing or claiming anything here, I'm just saying that I can't wrap my head around these concepts.
Love your remark! I find these implications rather fascinating and mind bending in their own right. If anything, they make it even more evident how time is a parameter so fundamental to human cognition that for us 'existence' is inherently a time-dependant property. I also suspect much of what we still haven't discovered in the realm of physics has to do with the limitations of a time-dependant representational system for concepts. Intriguing stuff to say the least ;)
@@AryaPhoenix Thank you for responding! I like how you state that our existence is time dependant. I've been obsessed with photons (and time) for decades and it never seems to get simpler and to imagine that in the realm of the photonic reference frame nothing exists at all gives me the heeby-jeebies. And yet here we are! My head hurts now. =D
@Adi Haran Stating that photons ignore speed (ie position) is an interesting (and it seems to me also correct) way of restating that photons ignore time. It surprises me that I've never heard any science populariser address these seemingly inevitable conclusions and I assume that the mechanism is well understood and involves something much deeper than popular science talks could cover.
I think this applies for all particles that move at the speed of light. We know that if i move at speeds comparable to the speed of light time ticks slow for me. If i move at speed really close to c(.9999999999999c) then time will be really really slow for me. This means that even my biological clock ticks slow. As soon as i reach exact c, time stops for me. Alll my cell activities stop. They just pause. I will be kind of dead. If i would be moving in a spaceship then i won't be able to control my space ship either. As soon as my speed falls below c time starts ticking again and i will be alive because my cell activities resume again and biological clock starts ticking again.
At speed of light indeed it seems time became "zero". Time "zero" = death = "zero" motion = "zero" 3D space-time continuum. Its a sort of "nothingness" ,"uncertainty" zone where everything is in a superposition state of a quantum wave function and where past, present and future coexist alltogether in the same moment at once. This state of motionless, massless, timeless, 3D spaceless is achieveable in "zero" absolute temperature too or at speed of light. The photon cannot start his journey to our eyes unless he "knows" some how that its destination is connected with its departure. The photon doesnt start the journey hoping it will have an ending point to receive him. The photon starts only and only if it has the final destination allready established. His journey, from its perspective, takes "zero" time and "zero" space distance from starting point to ending point...
I want to see Navier Stokes equations, IN THREE DIMENSIONAL SPACE.
I know its a bit out there.... at least it kinda feels off topic, idk.
Great 👍
Thanks
Short question @Brian please.
Which App do you use for the presentation of your hand written stuff on the iPad Pro?
So great an amazing
If u would continue with relativity it's alright but pls try to take up quantum mechanics as well and pls make a video on heisenberg's uncertainty principle or schrodinger's equation or diracs equation
here’s another way to think about it: the speed of light doesn’t change as you move towards/away wrt. a light source, okay. But it’s (apparent) wavelength (λ) and therefore it’s momentum (p = h/λ) does change! As you go towards the light source it will blue shift, as you go away, it redshifts. So when you think in terms of momentum instead of speed, it “coincides” with the inuition, although in a different way.
Also, there are a lot of implications because of this: as you travel towards a light source near the speed of light, it will blueshift into gamma radiation. So unless your spaceship has some sort of protection, you will burn to death.
Would you care to add the change of frequency for approach vs departure?
Fantastic and fascinating video. Are you taking requests for ideas?
I would love to see a more detailed explanation of a spaceship crew watching someone fall into a black hole. I’ve heard it said the people on the ship will never see the other person cross the event horizon. Due to time dilation he would appear to move ever more slowly, infinitely so. But, what does it look like for the guy falling toward the event horizon? Would it appear to him that clocks on the ship are moving ever faster, infinitely? Would he see see the universe expand as outside his gravity well clocks are moving infinitely fast?
It's from The Elegant Universe... The illustration..... 🌹
Gets really crazy with universe expansion as I’ve been thinking about...
Can we please do the Bose-Einstein Condensate?
That's not an equation
@@RR-gr1nigood one buddy
thank you very much for this series :-) love from Iran, and hope that all nations beat this corona virus
I thought I was only uniformed but my curiosity is not ambitious enough yet to do the discipline plus also may not be able to reiterate into a simplistic way to comprehend this? Now, if I do not pursue to understand then it indicates I am not only stupid but ignorant. Good thing I have a sense of humor so remain getting a kick out of this. I am getting an idea of why my wife gets mad at me. Thanks
I'm glad poor Gracie only got an egg thrown at her in this video.....It used to be a hand grenade. LOL.
Ok, but what speed are we measuring here? Speed from the perspective of an outside observer? Speed from the perspective of one of the moving points/objects? Objective speed from whatever the perspective is?
So if one particle is "escaping" with 0,9999999995c speed and a photon is "chasing" it with c speed, according to this equation the speed of approach/"catch" is still equal to c. That doesn't make sense.
The result is c for each case when one of the original speeds is c and the other is whatever less than c. So regardless if the "escaping" particle would move 1 mm/s or 99,999999999% speed of light, the chasing photon always approaches it with the "catch" speed of c? It's not true.
Would like to see this used to explain the GPS satellite correction
I believe that you also need to take GR into account when correcting GPS time. According to GR time runs slower in a larger gravitational field. So it runs quicker in the satellites. But due to SR it runs slower because they are moving. You need to use both SR & GR.
Excellent!, my only problem with this correction is that does not seem to work for c-c (if you run away from c at c), because, according to the equation, this will result in "0" or undetermined, while relativity claims that should be "c". How this equation reconcile relativity with "0" that means that c gets reduced to 0?
Let's say you have two light sources: light A and light B. It takes 10 seconds for light A to reach the starting point of light B and it takes 10 seconds for light B to reach the starting point of light A. If both lights start traveling towards each other, what will happen than? Both lights will travel 299.792.458 m/s, so the total distance each light travels in 10 seconds is 2.997.924.580m. How do both lights still reach the starting point of the other light source in 10 seconds, if they cannot approach each other with twice the speed of light? Do they somehow slow down? Are they going to take more than 10 seconds? Does the travel time stay the same? Does the distance somehow decrease?
I'm by no means an expert on these things, but it's still interesting. Hopefully someone can give me an answer to my question.
please tell us about general relativity's equations and also dirac equation
My 8 year old daughter says the following: ( in her own words)
It is not the speed of light that changes. It is the position of the observer (Gracie) or distance of travel. If Gracie run towards George the distance the object, whatever that object is, even light, it has less distance to travel. But when she runs away the object has to travel further. Therefore Dad, it is not the object that changes speed. What changes is the distance.
OMG, you and your daughter should understand that your "explanation" is the naive result (at 2:40).
@@erwinmarschall8879 thank you.
Sagan gave an example of him on a bike and a horse and buggy approaching an intersection and how “ time delayed” and confusing it would be if their images crossed the intersection before they did.
With more than 2 speeds there is problem with associativity in the relativistic case. Which is the correct answer?
Sir I'm getting answer in negative when speeds are high and the object is approaching towards the source? What is the correction here .please answer
Sir
We all know that speed of light is constant everywhere.
The question is........!
Why Refrection takes place when light travel one medium to another Medium?
What happens when 2 photons are head towards or away from each other. Also if time is malleable when near massive bodies and/or when passing near a singularity then it's speed would most definitely be variable as per the fact that speed itself is a result of the dimensional factor of time. Genuine question, not harassment. Thank you! I am a huge fan of your work!!!
*heading
If both “v” and “w” are equal to “c”, I can see that, applying today’s formulas, if the two beams of light run towards eachother the result is “c” but if they go towards the same direction the result is “0/0”. What does it mean? Thanks! Leonardo
then i think you need to work with Limits (from something like the equitation in 7:55 ) w ->c and if i`m correct by Lhopital rule it will be C
Vldi Grigoryev thanks!
Awesome explanation Professor Greene. One thing though, how did Einstein and modern science actually prove these bizarre but fascinating effects of relativity to be facts experimentally? Is it even possible?
Things like the LHC could not work if relativity were not true.
I pointed 2 flashlights at each other and slowed time by half since they reached the mid point at the same time it took one beam to go twice the distance.
Then I pointed one flashlight behind the other flashlight and broke time because I divided by 0.
what about when 2 beams of light approaching each other?
that way the denominator would be zero and the whole thing is undefined.
or is it impossible for an observer to have a velocity of c hence this situation doesn't exist?
Light at a constant speed. An analogy I'm thinking of is the maximum RPM of a gear because the set number of teeth on that gear. So at the beginning of the Universe, light took a while to get to that constant speed (RPM)...
Could you also do an episode on Ramanujan Summation (sum of all natural numbers = -1/12)? I know this result gets used in String Theory, but if you agree with the result -1/12, then how to make intuitive sense of it?
I remember a little about that. That 'Sum' is not the sum we see in daily life. It's another math operation.
Where did the magic correction come from? Why is it /1-(VW/Csqd), you could argue that once you have decided that light can only travel at 300,000Km/s then you need to manipulate everything to fit that requirement.
Entropy and Poincare's recurrence theorem...please
hi sir I want to ask if gravity is stretching of space time fabric due to mass . lets consider universe is expanding then, will it become thinner and thinner in dimensions like when we expand or stretch rubber like elastic fabric? if it does get thinner every time should mass stretch it more and more by same mass like mass on fabric does? if it does stretch more and more, like we know planets are rolling around the sun due to gravity will they roll more toward the sun or they will go away cause universe is expanding. i'm not able to explain this question i think correctly can you help me sir? what will be result will they fall into sun after some years or will they get out off the orbits and leave solar system ? is it related to dark matter?
Does the finite light travel time and therefore gravity propagation time have any effect on the shape of the Earth’s orbit around the Sun bearing in mind that the Sun orbits around the Galactic centre and it takes 8 minutes for the gravity to reach? Would we see any orbit distortion on a careful look?
This feels a bit like fudging the non-relativistic equation only to avoid a glaring paradox regarding c being max speed. The reasoning here starts with the desirable outcome and then it includes a sort of a fudge factor in order to "prove" the stated outcome. I would like to know if this can be derived in a mathematically disciplined way, that is based on assumptions which had previously been proven or otherwise been obvious.
How did he get the correction formula?
What happens when the torch carrier is moving?
I'm completely lost here. How can we combine two separate objects speeds and talk about them in single formula. What if two beams of light travel in opposite direction approaching each other ? They will do the same distance twice as fast ? Wouldn't they ?
Hello.. I am trying to find a formulation of the energy conversion theory by comparing an electrodynamic system, with the disposition of the quantum fields that determine center of mass variation, according to the theory of general relativity and the velocity of the center of mass in a stationary system (here the energy conversion is done), being a transition system, we can call it a reversible system, which ensures the variation of the center of mass, according to this theory of system reversibility.Through this theory, the conversion of energy in a reversible system will be formulated. This property of the system will give continuity to the assimilation of the energy flow, which arrives from the space below gravitational wave shape. Thank you!
How is the sun's spectrum shifted blue on the leading edge of rotation and red on the trailing edge of rotation facing earth when its light spectrum should be even over its entire surface?
Does the relativistic velocity combination law point to the expansion of spacetime? Is spacetime expanding at the speed of light? It seems to me that if spacetime is expanding from every point in space at the speed of light all matter embedded within spacetime would be subject to its effects including proportional gravity in warped spacetime.
Suppose they throw the eggs at equal speeds to each other. Then w=2v/(1+v^2/c^2)=2vc/(c^2+v^2). If the distance between them is D, is the time for the eggs to crash into each other given by t=D/w? But according to Galilean relativity it would be t=D/(2v)?
Cover 3-brane collisions.
OK, so all we have to do is find a way around that formula and space age can begin.
Magneto-Hydro dynamic equations
I'm guessing this is the actual correction everyone's always talking about with satellites.
Thank you! can you explain please how einstein got to this equation?
I was waiting for that too. Probably too difficult for us.
It's a little bit complicated, but if he keeps this up he could totally get to it I think. Keep following along.
light speed is just the speed that the universe communicates with itself. Think about two electrons and the charge between them. How fast does that charge travel. Doesn't matter what speed the electrons are going. The information about one electron that the other electron gets travels between each other at light speed. The universe communicates with itself at light speed. It's really all about the speed of causality. Light just also happens to travel with that speed.
@@dankuchar6821 thank you!!
Thank you for your description.
What this formula is saying is, we will never be able to research universe further than Alpha centaur maybe.
how about HEISENBERG UNCERTAINTY equation?
How about the E8 theory?
❤️👀
My guess would be, because light has no mass. (From what i see on the surface). But, i know underneath it all there's a-lot more depth to the answer. Otherwise, there wouldn't be the most complex math needed to measure those properties.
But Gracie would still have more time before the light reaches her, right? If she runs away.
what is the most mind boggling theory in physics according to your perspective?
If that was light traveling instead of a ball, if he runs towards the light, the light will reach him faster than if he runs away from the light.
Could you say the speed of approach isnt a real speed at all? Well i guess thats why its relativistic, cuz with normal speeds it does have an effect. But C-W and C+W it isnt actually adding to the speed at which the light is moving, or at which W is moving. The space between them shrinks faster but that is only because they are moving towards one another, neither speed is actually increased. So of course it doesnt approach you faster or slower, because nothing is happening to its speed. However, is saying that it doesnt approach you faster or slower, the same as saying, if you are moving towards it, you will collide sooner than if you were standing still, or later if moving in the opposite direction? I mean really its not the light thats doing the approaching, (i mean light is always moving sure) but its either complete darkness or light moving at 3million meters a second. So since its constant the only thing that can change, is YOUR approach to IT, which is why it doesnt approach faster or shorter, but still gets there in an increased or reduced, time frame. Right? Im not a total idiot am i xD im also not quite well versed enough to be able to do "perspective problems" and understanding precisely what happens in the same situation, from a different perspective, on paper or in my head haha
How did Einstein made the correction?
OK, so I get that two people approaching each other close to the speed of light will never see themselves getting closer at a rate that exceeds the speed of light. But what if there was a stationary observer watching these two people approach each other close to the speed of light? Would the stationary observer see them approach each other at a rate faster than the speed of light?
in this case nothing exceed the speed of light?
i really forgot my math. What Math used here, is this algebra or?
An equation a day keeps the doctor away
OK, then what you are actually doing when you are moving? Lets imagine, that a beam of light has started its movement in my direction from a distance of one light hour. So it doesn't matter whether I move towards it or away from it, we will meet each other after 1 hour, since our combined speed is C. But during that hour I can shorten or increase the distance between us. Is it an illusion? If it doesn't matter in which direction I move, can I say, that the distance between us stays constant? So I can say, that I don't move. But I can move sideways. If I step left or right, the beam will miss. Does it mean that sideways movement is the only movement possible?
It is not the speed of light that changes. It is the position of the observer (Gracie) or distance of travel. If Gracie run towards George the distance the object, whatever that object is, even light, it has less distance to travel. But when she runs away the object has to travel further. Therefore, it is not the object that changes speed. What changes is the distance and time to cover that distance.
Minor mistake in 9:59. I think there should be just "16/25", not "16/25 c".
Good catch.
Can the paradox of expanding universe be explained by revising Newton' s. Universal Law of Gravitation , so as to include complex number valued masses so that it can be repulsive also. Normal matter constitutes only 4% of the universe whereas dark matter can consist of imaginary number valued masses.