Relativistic velocity: When 1 + 1 = 1 

PBS spacetime and Fermilab uploaded a video in the same day. You guys just made my day.

Love the colour coded formula. Makes it quite a bit easier to follow.

Where were you during my university days ? You're helping me understand stuff in my later retirement life where at this point only helps in my understanding of PBS Nova episodes ! That's good enough though. Thanks.

Those comments at 1:50 are hilarious. I was shocked by the 2nd, but delighted by the 3rd: " Sorry, we dont serve fundamental particles. A Tachyon walks into a bar." Great joke xD

The way u explain things is fantastic. Just want to say “thank you” sir

Your last few videos explaining the misconceptions of relativity have cleared up the misconceptions. These are great videos. Thank you for sharing your knowledge.

Geno got roasted lol

Wow, what a great explanation of such a fundamental and important point about how velocity works! Thanks so much for this great video!!!

That is disgustingly awesome especially when I collapsed the terms with you had me grinning at the simplicity of the final result like a punch line to a good joke. I had wondered back in school about this oddity but never got the answer since they don't teach the transformation let alone things like Prime, un-prime and the third observer. It didn't help they still call these things paradoxes.

I love this channel!!!! Dr. Lincoln will always = #1 in my book no matter what speed we're going! :-) ~peace

Thank you for this video. It looks so simple, but I always get confusion on this subject and you helped to understand this.

Great video as always . Looking forward to the next one.

The equations are much easier to follow now, great work!

Relativity elongates the length of Fermilab videos

Thanks for sharin' what your'e thinkin, Dr. Lincoln!

Dude, you rock!!!

I just came from a need-to-revisit Spacetime expose on Noether's theorem, and now this! The four dimensional divergence of an anti-symmetric second-rank tensor equals zero... and there was light. That was my celebratory tune.

Nice as always. Where were you when I was a lowly undergraduate in Physics? You, Dr. Lincoln, should have been a teaching Physicist, students would have loved your style.... Great video, thanks again...

Thank you so much to make me to understand the concept of relative velocity. Before seeing this video , i used to think if a car is at rest and velocity of light from head light is c, then velocity of light from head light for moving car at velocity v, would be c+v

thank you fermilab.

Good time of the day to you Dr. Don Lincoln. First thank you and the Fermilab staff for all the videos you made, I finally got through all 92 of them in the playlist. Second, on the theme of relativity and speed: there are one question answer on which eludes me for some reason - 2 person travel on speeds near the speed of light towards each other, I am the un-primed observer, how do I see the combined speed they are closing? More precisely, how do I use the Lorenz transformation to calculate that?

The content of RU-vid has changed a lot in 10 years

My favourite bit coming up, when I go from nodding along saying "yup, got that" to throwing a notepad full of broken equations onto the desk three hours later. Right, where's that pen?

Love these videos

5:45 This is a very important point. There is only one way to add velocities and it is the relativistic equation he derived. As he said, We don't use the complicated denominator in our everyday world because the speeds are so low that it is essentially one. All too often I hear people, even fellow physics instructors, who have marginal understandings of Special Relativity, talk about the relativistic addition of velocities equation like it was a separate equation that only applied to relativistic velocities. It doesn't, it is the ONLY way to correctly add velocities. In case you are interested, the denominator you would get for two cars moving toward each other at 60 MPH is 1 + 8.0 x 10^-15, or 1.000000000000008.

That was very helpful understanding this problem.

Don Thank you for all the video's. What speed is the positron going when the boson decays?

Great video.

I wouldn’t even mention the previous comment by geno. He’s obviously someone who is entrenched in his world view adamantly unwilling to change. That type doesn’t come to these videos to comment because they misunderstood something in the video, they do so because they feel threatened by concepts they don’t understand and refuse to accept. You aren’t going to win them over, because they refuse to listen or look.

Ah! Loves me some Doctor Don!

A little deeper into the math than Dr. Lincoln wanted to take this (I can assure everyone that _he_ knows all this), starting from the formula at 5m27s: v[rel] = (v₁ + v₂)/(1 + v₁v₂/c²) This simplifies a little more when speeds are put in terms of fraction-of-c: β == v/c -- so that v can go from -c to +c, and β goes from -1 to +1. Then you have: β[rel] = (β₁ + β₂)/(1 + β₁β₂) Finally, there's a parameter that characterizes speed, and that can go from -∞ to +∞. And it's something that actually *does* add when combining velocities in the same direction. It's α = tanh⁻¹(β); that is, β = tanh(α) As v goes from -c to +c, β goes from -1 to +1, and α goes from -∞ to +∞. And the slope of α in terms of β is 1, at 0 velocity. So, e.g., when v = 0.01c, β = 0.01, and α = 0.01 - (about 0.00000033) And when combining v₁ and v₂ , the v's don't exactly add, the β's don't exactly add, but the α's *do:* α[rel] = α₁ + α₂ One thing this helps to conceptualize is that, while looking at v's makes us think there's a barrier of some sort that just won't allow v to get to c, let alone exceed it; when you look instead at α's, you see that there's no limit to that, and that accelerating really *does* keep you gaining steadily, not in terms of v, but in terms of α. IOW, *_trying to reach the speed of light is really exactly like trying to achieve infinite speed in Newtonian mechanics._* Fred

Great vid ! Can we have one about delayed choice quantum eraser, delayed entanglement swapping...?

I have a question about electron jumps around the nucleus. When the electron absorbs a photon and goes to the next energy level, does the electron jump without being in between the energy levels?

Can anyone explain how does that velocity equation work with speed that isn't parralel to the direction to other object?

So does that mean the Z boson, even though it is neutral, is actually charged (containing both an electron and positron's worth), only revealing so upon decay? Does that mean charge is a property of mass then or are there massless particles with charge? Tough wrapping my head around what charge is other than one of the several quantum properties like spin.

The z boson thing at the very end left me really confused. Did you explain all the details of this in another video? Because what the z boson is doing and what the electrons are doing seem really disconnected.

Nice explanation. It's any energy lost during the decay of Z bosons into the electron and antielectron?

It wasn't mentioned in this video, but does absolute value play into velocity and relativity?

Don Thank you for all the video's. What speed boson decays?

02:10 Must be really _cool_ to drive a convertible rocket. :o)

Very-well presented. Not that I know what I'm talking about.

What happens when a blackhole loses mass? Does it convert into a neutron star or something else entirely or even explode?

I stand in the Middle and V1 flies away from me with speed of light. In the opposite direction V2 flies away with speed of light. The distance that grows between them is V1+V2, is this different then 2C?

I think an eg. copper hoop accellerated from the inner half by a supperconductive magnetic accellerator in space , no resistance constant cohersion added by the momentum and centrifical force might exceed light speed.

Question: Assume there is one stationary observer A in the middle of straight line path between the two head on moving bodies, F and G, each at speed 0.6C. A does not know about G. He is just observing F. Also assume there is another stationary observer B away from the straight line path observing both moving bodies F and G. F starts off first, then after a little while G sets off. For observer A, would he notice a reduction in speed of F as G takes off? Would observer B record 0.6C for both F and G independently?

Why your Lorentz Transform formula uses plus sign, while others use minus sign?

I have a question.if a man on earth sent a message to a spaceship travelling 99.9% the speed of light if ron is in the ship and don is on earth can they interact?and if so would each know the other is seeing time different?

But why is c the limit though? (Not why we can't go faster, but simply why it is the limit.)

But closing speed for distant observer(me watching 2guys trying to collide with speed of light each) is still double the speed of light(if v1 and v2 have their speed c)? Am i right? Also i get , that this doesnt violate any law.

But what is the resistance to not having speed of light or more?(require logic)

So, big V's and little v's are in the numerator, but all the V's get cancelled out, and so light speed is greater?

How does it work when they are traveling at an angle to one another

And Tachions? They (supposedly) travel at velocities faster than light, don't they?

I love that shirt!

4:50 Don and Ron observe a velocity of 0 for themselves. So the velocities v1 and v2 are a cosmic reference frame? But I thought that didn't exist.

So wats really happening when 2 ppl come at each other at the speed of light if they always see the other person as going no faster than the speed of light? If thats true are they really only going half the speed of light toward each other?? Or do the collide at twice the speed of light

If two sun facing each other than their meeting point can before 4 minutes?

Traveling faster then the speed of light is like getting information before it is available, you can't do it.

Einstein's big think that time was not fixed still blows me away, its goes against all our everyday experiences

what is the song music in the beginning of the video ,:intro one

Does it apply to all vectors

Ah you explain it so well I understand where you're going why this is true before the halfway point even 😀👍

The calculations went a bit over my head. The graph helped make sense of the apparent "paradox". :)

Sir, I have a doubt. If I move opposite to a ray of light with some velocity 'v'. Then, should I move forward in time?

Amazing

Here you used Lorentz inverse.... But why ? Or they must be same because all inertial frames are same.. I am confused please help

Hey Dr. Don. Give us some words abaut the sterile neutrino measurement

I think it needs a simple explanation without equations that tells what is actually happening. It might be easier to say that the distance is changing or the time is changing.

I would tell all my friends but they would think I'd completely lost my mind.

Dear Dr Don, as You speak about relativistic velocities, is it true the conclusion that very fast traveling baseball ball (fraction of c) would act similarly as elementary particles act, in double slit experiment?

Hey, I need your guy's help! I'm gonna get a tattoo that says "how to build a universe" and some relevant physics equations following. Which ones should I use?

Something screwy with the red “relative” curve at 7:06. It appears to rise briefly above y=1 around x=0.9 and then dips back down to end at 1. The equation doesn’t support such behavior, and neither does theory if I understand correctly.

Is this reduction of closing speed a product of length contraction?

Hi. I have never learnt physics but I love it, so I listen and read everything about it. I am a special education teacher. Nothing to do with physics. But I love "space", and the bible for astronomers is:e=mc2/Thanks for the videos.

Third comment @1:52 is soooooo good

Awesome

We all know we cannot treat an electron cloud around an atomic nucleus classically like a planet orbiting a star. Nevertheless, sometimes in basic physics college course homework exercises, we DO use the classical model as a useful approximation. So, what happens to Coulomb's Law: F =k* (q1q2/r^2) in vector form? Is that still a useful approximation? If so, then why aren't electron clouds ELLIPTICAL (like planetary orbits are) around atomic nuclei? Obviously, the chance is zero that the initial velocity of the electron around the nucleus just happened to be that singular value that made its orbit perfectly circular. All other initial momenta & distances from nucleus would yield an elliptical orbit. Furthermore, doesn't the concept of "spin" of electrons apply also to protons, neutrons, and all other particles? It seems strange to me if only electrons had spin.

If two spaceships travel towards each other at 0.75c as observed from Earth then the equation given in the video states that on board either spaceship they would both see the other travelling at 0.96c. That makes perfect sense. However, what about from the frame of reference of the stationary observer on Earth? At what speed does he/she see the ships approaching each other? Does it even make sense to ask this question in the context of relativity? Maybe it is not possible to measure this from a stationary reference frame? If anyone knows the answer please help!!

AWESOME

But is it the velocity seen in any reference frame? Ron according to you

How is the speed of electron measured from Z boson's ref frame? Hope its not using relativity. Anyway great video

Thanks. ! !!!!

How do the two people moving toward each other measure their closing speed? By the redshift of light coming from the other?

I still don't quite get time dialation tough. Suppose a scenario: A and B are close to a black hole at the same height from it. A is orbiting the hole with constant (relativisticish) speed in an circular orbit and B uses rockets to hover in place. Who experiences the time dialation? (The dialation from the gravity well itself can be ignored since both are affected by it equally, right?) My quess would be A is affected more since it is actually moving. Then again acording to Einstein A is actually just moving in a straight line. B is accelerating constantly and if I had to judge, its B that is doing any reference frame hopping, tough that concept too is bit nebulous to me.

I loved the dude commentary....LOL Physics always win....even if we don't know all...yet...^^

if a spaceship travelling at the speed of light, and projecting the light beam forward & backward respectively, what will happen to the time inside the spaceship from your observation ? still ? 2x of you ?

Need to add something to this. Yes, you're absolutely right. However.....thought experiment. lets say the spaceships that is moving towards you has a very large rule attached and extending far in front of it, This rule moves past the windows of our spaceship and we are able to read the measurements of the rule at two times. We would find that at high speeds, the gradients of the ruler have actually shrank due to Lorentz contraction. So, even so if we were to calculate the speed using the distances expressed on the rule by, say by measuring the time that each 1 meter line went past us, we might end up with a result many times faster than C. This would be incorrect measurement, as travelling at this speed, the meter according to the moving rule is much smaller than what it would be at rest. The implications of this are that if it was possible to travel in a spacecraft able to move at such speed are that it might be possible to travel to any point in the visible universe in a relatively short amount of time (excluding effects of particles hitting the front of the spacecraft!). the universe shrinks in the direction you are travelling... 1000's of light year distance is compressed to much shorter distance, and this shorted distance appears to be passing you at a speed less than C. When you get to your destination the other side of the galaxy, in just a few hours, you marvel at the technology that has enabled you to get here in your own lifetime,. However. From an observer who watched your spacecraft depart, from his perspective, it has taken 1000's of years to travel. and if you traveled back, you would find a place 1000's of years into the future, even though for you, you'd have only been away for a few days.

I'm troubled by this - you're talking about two observers moving toward each other at the speed of light, and what it would "look like" to each of them as to how fast the other seemed to be moving. Let's say they were each moving at only 50% the speed of light, so they are closing on each other at exactly the speed of light. Wouldn't this cause a Doppler effect, so that the distance between them seems to close at the speed of light, but the wavelength of light they are "seeing" is an extremely short wavelength as they approach, and extremely long as they part? Wouldn't they "see" or perceive themselves closing on each other more quickly and parting more slowly - but with a huge shift in the "color" of the light? I think I understand the math, but I don't understand thinking of it as what they'd be seeing. It seems to me that if I was one of those guys moving toward each other at the combined speed of light, it would "look" like the other guy was coming at me at twice the speed he moves away from me when he passes - IF I could see the wavelengths of light I'm receiving. But, instead, wouldn't I be receiving light with an incredibly short invisible wavelength as we approach, and then an incredibly long invisible wavelength as we recede from each other? Doesn't the whole premise of trying to express what it would "look like" make this a completely non-sensical exercise? Wouldn't it "look like" an intense flash of light above the visible spectrum coming at me on one side and then a flash of light below the visible spectrum on the other side? I guess maybe I'd be "seeing" the other guy's far-far infrared signature as visible light coming at me and his far-far ultraviolet signature as visible light going away from me? I guess I have to do the math on that - what's the Doppler effect on the received light?

An observer might be moving with two velocities according to two different observers So if the statement 'faster u move heavier u get' is true What is the gravitational force created by that observer

Whenever I see the Einstein's toungue Out photo I feel that he is teasing me by proving the world wrong

How I can write e-mail to author? Thanks.

So... what I don't get is this: Suppose there is a light source and a stationary wall located one light year away. of course, it will take the light one year to reach the wall. Now, assume that the wall is moving with some speed towards the light source as the light takes its time reaching it... now, the total combined speeds of the light and wall are less than the speed of light... so... the light will reach the wall after more time has elapsed even though the wall is making progress towards it, compared to being stationary with a combined speed of the speed of light? I'd like an explaination because something must be wrong here!

It's much simpler to explain. Lay down meter markers (rulers), slowly, taking your time. This is space to a stationary observer relative to you. Now, go back to the beginning and start applying acceleration with a constant experienced force. You will accelerate indefinitely, perfectly, according to regular old Newtonian F=ma, well exceeding "c" in terms of meter markers you see crossed per second. When you understand this, you will understand special relativity. It is this phenomenon that will allow space travel to remote locations without excessive aging for the traveller. It will be another story for the ones you left and returned to.

Is the velocity here is negative? Because of which the equations are positive...

legend

phisik is every thing:)

What about relativistic mass? If you're traveling half the speed of light and an object is travelling head on towards you also at the speed of light, is your relativistic mass different relative to that object because you are approaching the speed of light relative to that object? Ok ok, .8 times the speed of light. Still enough for a relativistic effect. So what happens to your mass? Is it dependent on your reference frame and if not, then what? Space itself?

TLDR: I think I must be wrong about high speed making you turn in the direction of the future, but I don't know why I'm wrong, and the astrophysicist I asked, didn't have time to debunk the idea during after-lecture questions. One reason people think the speed of light can be broken is that they think it is a barrier, like the speed of sound. For a While now, I've been thinking of time, and the future, as a direction you turn in as you get faster. So, if you push your spaceship faster, you start heading forward in time, by turning in the direction of the future. This explains why you can't "break the light barrier" and explains time dilation, since when you push harder, you go into the future faster, and, since speed is distance over time, by definition, if you move in time as well, you stop going faster. This explains length contraction as well, since part of the length of your spaceship is in the "future", and part in the "past". This also explains the non simultaneity of events, since different parts of your ship are turned, continuously, over a distance in time, so the front of your ship passes the barn exit in the future relative to the rear of your ship. I have not yet worked out how to think about how this would affect time dilation between ships, since ships heading towards each other would both be turned towards each other in space, but also, both towards the future in time. One possible outcome of this is that gravity could be created as a byproduct of the way that matter interacts with space-time. If the time-motive force is a thing in time (I'm not sure that it is used in modern physics), and a river of time is flowing past all matter, and the matter slows that flow, then the pull of gravity might be related to the way we are pushed towards the future, towards the planet, similarly to the way the gravity of a black hole makes the centre of the black hole the future for all particles within the event horizon. In four dimensional space-time, this conceptually seems to make sense, but I'm an engineer, not a physicist, so I don't know what the math says. Why is this conceptual framework wrong? I did manage to ask a young astrophysicist this after a public lecture, but it seemed to be such a foreign concept that she didn't have any kind of framework to explain why I was wrong, so it seems to be either too far from the abstract to explain why it is wrong, or so wrong that the concept isn't even taught as a failed old idea in classes.

Made it all the way through the Special Relativity videos and basically agree with everything you have said. Of course one can never disagree with experimental results, so I don’t. However the Lorentz Transforms do not quite explain everything, a few slight modifications on the quantum level would transform everything into a logical and intuitive process and unify quantum mechanics with relativity. 1. Removing the quantum fluctuations in various fields that always produce random results, which can be explained separately, everything in quantum mechanics suddenly becomes relative. 2. Probability with the randomness removed becomes deterministic. 3. Uncertainty with the randomness removed is relativistic. 4. Time is a dimension, but the expansion of the universe should also be figured into the time equation; which means that light travels at the speed of light times the expansion of the universe. 5. In Space (not STC) the angular momentum of the speed of light is always conserved. Yes, even Baryonic particles’ fields angular momentum = the speed of light. 6. A particle’s location and shape become relative to the observer at close to the speed of light. 7. The root cause of all relativistic effects is an egg-shaped shell of degenerate pressure surrounding a relativistic location. So my only disagreement with the video series is… “The slower you travel at the speed of light, the faster you travel through time” - If something doesn’t make sense, then it is probably not true; so I am going to say it doesn’t make sense. What I would say is “The conservation of the angular momentum of the speed of light is always conserved, that angular momentum causes our perception of time in the matter.” And the Lorentz Transforms should produce an egg-like shell. These concepts are testable by using many “Observers” not just one measuring stick.

Cool. I was constantly wondering if there is a possibility of double speed of light from the opposite directions. Now, I not yust know the answer, but I also understand the question. Thank you.