The goal of relativity is to explain and understand

how motion looks from different perspectives, and in particular, from different moving perspectives. It’s easy enough to describe motion itself

– if something is moving relative to me, that means it has different positions at different

times, which I can plot on a spacetime diagram. This straight line corresponds to motion at

a constant velocity of say, v units to the right every second. And the question we’re interested in is what

do things look like from the moving perspective? Of course, the answer to this question is

a physical one, and is determined by experimental evidence gathered by actually moving. And that evidence will come into play, but

first we need to understand what it means, in terms of spacetime diagrams, to view something

from a moving perspective. We’ll start with a key property of spacetime

diagrams: when someone draws a spacetime diagram from their own perspective, on that diagram

they’re always, for all time, located at position x=0, since they’re always a distance of 0

away from where they are. Or in other words: a spacetime diagram like

this represents your perspective only if your worldline is a straight vertical line that

passes through x=0. If, on a spacetime diagram, the worldline

describing your motion leaves x=0 and goes anywhere else, that means you’re moving relative

to the perspective of that particular diagram, and thus it’s not your perspective. With this in mind, to describe how things

look from the perspective of a moving object, like this cat, we simply need some way to

transform spacetime diagrams that makes the worldline of the cat into a straight vertical

line through x=0; or in other words, we want to make the spacetime diagram where the cat

is moving into one where the cat’s worldline coincides with the time axis. That’s not something we can do just by sliding

the whole plot left or right or up or down, like we’ve done for perspectives from different

locations. No, changes of velocity require some sort

of rotationy thing to change the angle of the worldline, and importantly, whatever this

rotationy thing does should be generalizable to a world line at pretty much any angle,

since there was nothing special about the particular speed the cat happened to be going. There are also two important pieces of experimental

evidence that we’ll need to take into account: first, if I measure the cat as moving at a

speed v away from me, then the cat will measure me as moving at that same speed v away from

it, and likewise if we’re moving towards each other. Which means we not only want to transform

the spacetime diagram in a way that the cat’s angled line becomes vertical, but we also

want the angle between our two lines to stay the same after the transformation – that

is, from the cat’s perspective, I should be moving. The second piece of evidence we’ll come to

later. Let’s focus just on the section of the cat’s

worldline from time t=0, where it’s at x=0, to t=4, where it’s at x=2. This section is a straight line between those

two points, and we want it to end up as a straight vertical line, so we can simply leave

the t=0,x=0 point unchanged while moving the t=4,x=2 point onto the time axis (where x=0). And there are really only three general possibilities

for how to do this: either this point gets moved onto the time axis while keeping it

at the same point in time, t=4, or it gets moved onto the time axis at an earlier time

(say, t=3), or a later time (like t=5). There’s a very nice geometric way to picture

these possibilities. If we think again of motion on a spacetime

diagram as a series of snapshots, like, at time t=0 the cat is at position 0, at time

t=1 the cat is at position 0.5, at time t=2 the cat is at position 1, etc, then the transformation

where points move to the time axis and keep the same time just looks like sliding each

snapshot over a corresponding amount; the possibility where points move to the time

axis at a later time looks kind of like some sort of rotation around the origin; and the

possibility where points move to the time axis at an earlier time looks kind of like

some sort of squeezy rotation. The reason these last two involve rotating

the snapshots rather than just sliding is to make sure that the angle between the cat’s

worldline and my worldline stays the same before and after the transformation – it’s

a fun little geometry puzzle to understand why. Now, among these three, the option that makes

the most intuitive sense based on our everyday experiences of the passage of time, is that

a given point in time should stay at the same point in time, and just slide over to the

time axis. I mean, we don’t noticeably experience time

travel every time we hop on a train or bike or plane. And this sliding does mathematically work

– if we move things at time t=1 a half meter to the left, and things at time t=2 one meter

to the left, and so on, then we’ll have a description from the cat’s perspective – the

cat’s not moving, and I’m moving to the left half a meter every second. It works for other speeds, too. If we want the perspective of somebody who’s

going a meter per second to the right relative to the cat, we can slide the snapshots over

even farther, and now the cat’s going a meter per second to the left, and I’m going a meter

and a half per second to the left. And of course we can slide back to my perspective

from which the newcomer is going a meter and a half per second to the right. This kind of sliding change of perspective

is normally called a “shear transformation,” but that’s when both dimensions are space

dimensions: since one of our dimensions is time, a shear transformation represents a

change in the velocities of things, so in physics it’s called a “boost.” As in, rocket boosters boosting you to a higher

speed. However, it turns out that boosts in the physical

universe are not actually described by shear transformations. This is where the second and most famous piece

of experimental evidence comes in: the speed of light. As you’ve probably heard, starting in the

late 1800s, physicists built up mountains of experimental and theoretical evidence that

the speed of light in a vacuum is always the same, even if you measure it from a moving

perspective. This is, of course, entirely unintuitive from

our everyday experiences with velocities, where if you throw a ball from a standstill

and then from a moving vehicle, the ball thrown from the vehicle will be moving faster relative

to the ground. And yet, experimental results show that light

does not behave like everyday objects: shine light from a standstill, or from a moving

vehicle, and its measured speed relative to the ground will be the same. Shear transformations simply can’t accomodate

this feature of light’s behavior: they change all velocities equally by sliding each snapshot

an amount proportional to its time. No velocity remains unchanged – if you draw

the worldline of a light ray and then change to a moving perspective using a shear transformation,

the speed of that light ray will change, which is wrong. Luckily, one of the other two options for

boosting to a moving perspective can accomodate a constant speed of light: remember the transformation

where the snapshots do a kind of squeeze rotation, and points move to the time axis at earlier

times? This kind of transformation can amazingly

leave one speed unchanged, even while it changes all other speeds. More amazingly, the unchanged speed is left

unchanged in all directions. Let’s do an example. Here’s a set of snapshots from my perspective

with a slow-moving sheep and two fast-moving cats, and let’s suppose that we have experimental

evidence that cats always move at the same speed regardless of perspective. If we want to describe this situation from

the perspective of the sheep, we can’t simply slide the snapshots over so the sheep isn’t

moving and its worldline coincides with the time axis, since that would change the speed

of the cats. But, if we slide and rotate and stretch the

snapshots like this, then look – we’ve transformed the diagram to both describe things from the

sheep’s perspective and keep the cats moving at the same speed they were before. You might note that the various cats appear

to be spaced out differently along their worldlines, but that just means that the constant-time

snapshots from my perspective aren’t constant-time snapshots from the sheep’s perspective. The important thing is that the angle of the

cats’ worldlines – which represents their speed – has remained unchanged. It’s kind of amazing to me that this works

at all; that it’s mathematically and physically possible for all speeds except one to change! But it is possible with these squeeze rotationy

things, and they’re the answer to our question of how to describe motion from a moving perspective. Well, not by keeping the speed of cats constant,

but by keeping the speed of light constant: by doing squeeze rotations so that a moving

perspective’s angled worldline becomes vertical without changing the speed of light – that

is, without changing the slope of the worldlines for light rays. These squeeze rotationy things are called

Lorentz Transformations, named after one of the first people to derive the correct mathematical

expression for them – it looks kind of like the equation for rotations that we saw in

the last video, and I’ll post a followup video showing how to derive this using just a few

simple assumptions and experimental facts. Lorentz Transformations are at the heart of

special relativity – they’re the thing that Lorentz and Einstein and Minkowski and others

figured out was the correct description of how motion looks from moving perspectives

in our universe, and they’ll be the foundation of the rest of this series, too. Now, as we’ve seen, Lorentz transformations

look different depending on what speed you’re trying to keep constant, or how you’ve scaled

your axes. Normally, physicists draw their spacetime

diagram tickmarks such that if every vertical tickmark represents one second, a horizontal

tickmark represents 299,792,458 meters, which means that the speed of light, which is 299,792,458

meters per second, is drawn as a 45° line – to the right for right-moving light, and

to the left for left-moving light. With this scaling, a Lorentz Transformation

that leaves the speed of light constant simply consists of squeezing everything along one

45° line and stretching along the other in a particular, proportional way. You can see immediately how this changes the

angles of all of the other worldlines, that is, changes how we perceive their speeds,

and yet doesn’t change any of the light rays. And it turns out that it’s possible to actually

build a mechanical device that does Lorentz Transformations for you: here it is! Just like how a globe has the structure of

rotations built into it in a fundamental way, and you can simply turn the globe to see how

rotations work, rather than doing a lot of complicated math, this spacetime globe has

Lorentz Transformations built in: it does the math of special relativity for you, allowing

you to focus on understanding the physics of motion from different perspectives! Here’s a quick example: from my perspective,

I’m always at the same position as time passes, while the cat is moving away from me to the

right at a third the speed of light, and the light rays from my lightbulb are moving out

to the right and left. Using the time globe, I can do a Lorentz transformation

to boost into the cat’s perspective. And from the cat’s perspective, the cat – naturally

– stays at the same position as time passes, while the cat views me as moving away from

it at a third the speed of light to the left, and the speeds of the light rays from my lightbulb

are still the same, still at 45° angles. I just love how tangible and hands-on this

is – normally when people are first introduced to special relativity and how motion looks

from different perspectives, it’s done with a bunch of messy, incomplete, algebraic equations

– but you don’t need the equations to understand the ideas of special relativity and how motion

looks from different perspectives. You just need an understanding of spacetime

diagrams, and a time globe. And so in the rest of this series, I’m going

to be using the time globe extensively to dive into all of the normally confusing things

you’ve heard about in Special relativity: time dilation, length contraction, the twins

paradox, relativity of simultaneity, why you can’t break the speed of light, and so on. I have to say a huge thank you to my friend

Mark Rober for helping actually make the time globe a reality (you may be familiar with

his youtube channel where he does incredible feats of engineering, like this dartboard

that moves so you always hit the bullseye). He devoted a huge amount of time, effort,

and engineering expertise to turn my crazy idea into this beautiful, precision, hands-on

representation of special relativity and I’m supremely indebted to him – this series

wouldn’t be possible otherwise. And if you’re eager for more details, I’m

planning another whole video about the time globe itself. In the meanwhile, to get more hands-on with

the math of special relativity, or economics, or machine learning, I highly recommend Brilliant.org,

this video’s sponsor. In conjunction with my video series, Brilliant

has rolled out their own course on special relativity with their own unique illustrative

scenarios – like relativistic laser tag to understand lorentz transformations. If you want to understand a mathematical topic

deeply, there’s really nothing better than thinking through the ideas and solving problems

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you can get 20% off by going to Brilliant.org/minutephysics. Again, that’s Brilliant.org/minutephysics

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Why is this man talking in 2x speed ?????????

I would prefere time in X axe

For a no english speaker, you talk really fast.

Perhaps videos with 2/3 of the content, but slowly, will be better.

Because are good

I mean.. i have about two more weeks of freedom

What am i doing here with linear algebra?!

I would pay money for a time globe for my desk. Just in case Mark Rober is interested.

The light speed is the same yes mainly because it doesnt have any mass to be pushed. But that doesnt means the speed of other changed. It just an illusion of other speed change because you rely on light to get information.

My likes keep disappearing…

Wait a minute, could you start again from the part about the cat, I lost you around after that 🙂

I graduated from university, I studied physics …. but only now I know what the hell Lorentz transformations were good for 😀 (besides driving students insane)

You talk way too fast. I can't look at what you're showing because by the time I've looked at it, you're 5 sentences later.

What?

amazing video

Actually, I find the algebra simpler.

My culture has shapes that I find over and over in the math of physics and fractals.

I'm thinking this isn't coincidence

aaand now i want a time globe.

WOOOOOOWWWWW! You're beyond awesome <3

@7:19, seems obvious. I was thinking earlier that “not everything perceives time symmetrically “

Some people think “today went so quick” and others “the day dragged on” time is not a constant. It’s a concept.

Now… show me how does this shifting will look in

three dimensionswhich is how the real world works. How does a 3D Lorentz transformation looks like so that light stays the same inall3D directions while all other things change.…angry bc i cant think of a way to get past the 45s…arggg.

To make sure I have this correct:

A Lorentz transformation is simply a change of basis operation between bases such that your line is transformed to x=0 & light lines are always at a 45° angle to both axes.

Also, the standard basis (meaning you are at x=0) would be:

{<299792458,0>, <0,1>}

Am I interpreting this correctly? Sometime there are math vs. physics terminology differences.

I want a time globe

plz use a de-esser

Very good explanation and I love the time globe. Thank you.

Can you please consider to do something in order to reduce a bit the sound intensity for future videos? I've reduced the volume on headphones and it is still so intense that I've switched to speakers. Thanks.

Just found out that a theater equalizer preset works ok)

just a 2 cents about the change of different spacing of the cat after the transformation. The speed stays the same but the wave length of light changes similar to doppler's effect.

I thought coordinates were (x,y) but at 3:13 you're doing (y,x)

I MUST HAVE TIME GLOBE

No object in our galaxy is motionless, let alone in the Cosmos.

X-Zero velocity is an absurd reference.

Really fascinating!

https://www.youtube.com/watch?v=6zWy6_Mog70 Here's a much better lesson on relativity that won't leave you scratching your head

The special relativity of One-Stone (Einstein) is …sorry, BULLSHIT ! It does´nt work !

Reletivity is J€₩!$# Bullshit Kabbalah that Albert Einstein plagiarized!

But the cat's speed in the mechanical example is not passing from the origin!!

2 hundred 99 million 7 hundred 92 thosand 4 hundred 58 minutes.

loved it

Bear with me, but the cats moving at C are rotated to the time axis and appear closer together. Is this what is known as a Lorentz contraction?

I don't understand. When you squeeze the lines, the light speed changes too? The light rays on the one arrow get squezed together the other more stretched out so the one light ray moves slower the other faster.

Is this what also causes light to red or blue shift as well?

Love the drawings.

Very interesting…

So the universal axis belongs to non other than… I AM THAT I AM. No?

Speed of light will increase as it approaches the event horizon. No?

Or; we could just agree, to agree,

to what the name of what 2 agreeing Physicists would be called… a ''Paradox.'' -9919

Wow for the first time in my 33 year old life i think i am getting special relativity

I went through much of grad school for my PhD in physics. I was always bad at relativity but it didn't matter because it wasn't part of my field. I ended my grad school with a masters and went into the private sector to work, and this is the first explanation of Lorentz transforms that has ever made sense to me. I need to go revisit my old books now.

Is there somewhere i can purchase one of those globes? I super-mega want one!

I have a question relating to the experiment done with polarized light. When the angle of the second lens is adjusted there is a nonstandard coralation as to how many particles pass through. Can your space time globe be used to track the difference?

Thats a cat?

that desn't proof y light can't vary in speed and don't let us know what happen to a photon trap…. Annoying when you realise Lorentz did a math trick to fit a theory and not to fit the truth…. And IT IS PONTCARRE not Einstein !

But how do you do it in real time frequentley while controlled.

Almost the default mistake with these videos. The tutor talks too fast.

Slide rotate and stretch – Einstein in your pocket!

Make the cat communicate witb a spider, then you got something.

OMG this is amazing!!!

It's true. Cats always move at the speed of light.

when you chase them with a squirt gun…

Time globe!!!! Wow

Been trying to understand this for years. The time globe gave it a visual model that really helped. Thanks

7:33

subliminal (more on this later) xD

Excellent! I think that "time globe" can be motorized for a more precise and smooth motion, and Mark can of course do it!

I like these educational videos, but why do they speak soooo fast?!

I really doubt you understand this either by the way you talk through this. It ain't true that students can't understand relativity because they only have been shown a basic few equations. It is like saying students can't understand newton's three laws of motion because they ain't using higher level math. And I don't know where you get your ideas on group theory.

THe first time I read a chapter on relativity I didn't think it was that hard. Maybe I didn't study it in depths like later classes did but it really wasn't.

Couldn't you do a Lorentz transformation without any physics. It just seems that if we had a set of vectors and wanted to find a T(v) such that it alters all but one of them wouldn't lorrentz transformation do that?

Wow. You are a great teacher.

I hate that I can hear this small "munching" sound whenever he speaks. It's fcking annoying xD

Oh, I see.

There are hyperbolic rails keeping the product of the eigenvalues constant.

c².

😵

shameless plug for ur sponsor. gross.

So Henry is not just abusing cats like Schrödinger did, he's mistreating sheeps as well.

this is excellent

Ex – Pear – iment

not

Ex – Peer – iment

Great job explaining complexity by simplicity. Can nuclear physicists and cosmologists do the same?

Thats great what I have visualised in plane graph paper you have established with a mechanical device

I'm sure most of the people watching this video are smarter than me.

But, why is the narrator talking so fast and drawing so fast?

I'm presuming everyone else understands this and it's just my ignorance

that is interfering with my understanding. I think I'll look elsewhere.

I could not stand to watch past 2:39, this is far better Suited to a “physics student” than to your average YouTube viewer. I hope you can accept it as constructive criticism that this Reminds me of all the confusion over particle versus wave i.e. wavicle; and except for very few or perhaps those using amphetamines confuses the issue needlessly. There is an animation it is made intuitively clear by means of a dimensionally aware (unfortunately I cannot reference it at the moment for you) but within a 10 to 20 CGI A substantial Demonstration of quantum insight is created rather than these linear contortions

Why bother with practical and experimental physics. Theories are easier. In a couple of decades there will be thousands of theories but not a single one would be practical. Rid yourselves of drugs people. Do something useful and practical.

7:10 what about the cats’ perspectives? How do you transform that?

Take 4 equal sides and form a square. One of the diagonals is “space”, and the other is “time”. Then you can stretch and squeeze the square into rhombi.

Too confusing–esp. with the narration going too fast.

Who in the history of humanity assumed that experimental results have perfect accuracy ? that relative velocity has to be v1+v2 (and not (v1+v2)*m + n where m is close to 1 and n is close to 0 and both could be some arbitrary functions of either v1 or v2 or even both). While special relativity provides a more accurate answer, it is not perfect either (check to 100 places of decimal and you'll find it is in-accurate). An even better theory than SR will turn out to be more accurate in future. A few decades later that would not explain the results and be replaced by an even more accurate theory to 1000 places of decimal. And the cycle of human innovation and understanding of nature will continue to grow more and better over time.

Prove that Lorentz transformation is valid in physics.

Submit your paper in PDF to claim an iPhone 11.

https://sites.google.com/view/physics-news/home/challenge

Henry:

You need to speak MUCH slower. You have a strident, nasal inflection in your pronunciation, and to compound your unintelligibility, you have a non-standard accent and you speak way too fast.

The net effect of this is the video is ruined.

I was going to ask about why the red/blue shift happens with light, then I remembered that is a frequency change, not a velocity change.

8:08 .. the sheep is moving 50 percent of the speed of light in that example 🤯

I don't know why they named it minute physics …..lol

Everyone knows time is a cube.

Simple linear algebra yields those equations fast. Less head scratching!

Cat exist out of time, freely moving, sometimes cuddles.

Are these transformations linear in the spacetime diagrams??

Doctor, my brain hurts.

Is there a resource available to help me understand the equations for when I need to calculate stuff

I clapped my hands whenever I understood something

then I realized I wasn't the only one in the restaurant.

xD

Hi. This video series is great! Thanks for doing these. I have one question. At 2:34, you say the angle between the cat's world line and yours needs to stay constant through the transformation. However, later when you show Lorentz transformations, the angle definitely changes. Why is this?

You are a very good explainer. Thanks!

I really liked the way you explained the spacetime diagram.. plz. Keep making such videos for us..

my friends its all beautiful but take the last minute of video and put it in front, and spare us the 6 min of all the bullshit. bla bla.

so like light is special right ?

What is a "light ray"?

As a 13 yr old I have literally no business watching this

You're amazing! Thank you!!! Keep up the great work ✌🏼

You changed the meaning to suit your narrative tho the lines and there meaning one the line was the subject the next the position the line was on was the subject changing the definition doesn't make it right

sell us the freaking thing!

Hi,

I'm a high school student looking into making the "space-time" globe to help explain the theory of relativity for my final physics project.

I was wondering if there is any instructions/resources I could use to make it.

Thanks.