跟读练习: Einstein Didn't Invent Relativity! - Physics Explained for Beginners - 通过视频学习英语口语

Hey what's up you lot, Parth here.

It's the final video of 2019, this is the last one I'm going to be making before the start of the new decade, and today I wanted to talk to you about who invented relativity,

or who discovered relativity, depending on how you want to view it.

But the answer isn't as obvious as you might think.

Now you guys have been asking me for a long time to make videos about relativity, about thermodynamics, and to complete the Maxwell's Equation series that I started a while ago.

I've done two videos on that already and I've got two more to come, but those will all be in the new year.

For now, I wanted to talk to you about relativity

and about whether Einstein was the first person to have come up with the idea.

So without further ado, let's get into the video.

Now, like I said earlier, when we say relativity, we automatically think about Albert Einstein as being the person who either discovered or invented it, depending on how you view mathematics and physics.

But actually, the first person who came up with that idea, as far as we're aware, was not actually Einstein.

It was Galileo.

Albert Einstein is famous for his work on the theories of special and general relativity.

But way before Einstein, Galileo had his own theory of relativity.

Now before we go any further, there's one thing that we need to clarify.

Einstein did not steal Galileo's relativity.

Einstein did not take credit for Galileo's relativity.

They're very different ideas, just similar concepts come up in it quite often, and they're based on the same thing.

I'm being very vague, but you'll see what I mean in a second.

Both theories of relativity, Galileo's relativity and Einstein's relativity deal with fundamentally the concept of relative motion.

That's the motion of one object or one frame of reference relative to another object or frame of reference.

We'll see what frame of reference means in a second.

Now whenever we measure the speed of an object we always have to measure it relative to something else, relative to maybe a reference point.

So when we say a car is moving at 50 miles per hour, 50 miles per hour relative to what?

50 miles per hour faster than what or away from what.

That away from what often tends to be the ground

or you know the surface of the earth in most cases

because it's always annoying to have to constantly keep saying I

was driving at 50 miles per hour relative to the earth's surface

and you don't want to always say that but the idea is

that there has to be some sort of reference

that we're measuring speeds relative to and this is where the idea of relative motion comes in.

So So if I were to be running at a speed of 5km per hour, which obviously I wouldn't be doing for very long,

I hate running, I would be running at 5km per hour relative to the surface of the Earth.

This means that if we were to pick a point on the surface of the Earth

and use that as our reference point, I would be running away from it at a speed of 5km every hour, assuming I actually ran for that long.

Or equivalently we could just say that I'm running at 5km per hour relative to the surface of the Earth,

which is the thing that we take to be stationary when we make measurements like this.

In this case, what we've done is chosen something known as a reference frame, a frame of reference.

Now, a reference frame has a very complicated mathematical definition, but we're not going to go into that here.

For our purposes, all we need to know is

that a reference frame is kind of like a coordinate system that we choose.

In this case, we've chosen a coordinate system that could, say, have its origin at the random point on the Earth's surface that we chose.

We could say that the x direction is toward the right, the y direction is into the screen, and the z direction is upward.

And the earth is stationary in this reference frame, because relative to our coordinate system, the surface of the earth is not actually moving.

Whereas me, the person running on the surface of the earth, is not stationary in this reference frame.

And the reason for this is that every, say, minute or so, my x coordinate in this chosen coordinate system increases, because I'm moving relative to our coordinate system.

However, the interesting thing about both theories of relativities that we're discussing here, both Galileo's and Einstein's theories of relativity, is that we could choose a different reference frame.

We could choose my reference frame to be the one that we look at this scenario through.

So one thing that we could do is to choose a point on, let's say, my face as being our reference point or our origin for a new reference frame,

because this point moves the same way that I do.

And so in my reference frame, that point is not moving.

So we could choose a set of coordinate axes that emanate from this point on my face.

We could choose the x direction to be the same direction as we previously chose, and same for the y and z directions, except that this point is now moving the same way as me.

And if we now transform our perspective, if we look at this scenario through my reference frame, then it's perfectly valid for me to say that in my own reference frame, I am stationary.

I'm not moving relative to myself or to our origin that we've now chosen.

but the earth is moving in the negative x prime direction.

We'll call it x prime because we want to differentiate between what we called x earlier and now we're calling x prime.

The earth is moving in the x prime direction at negative 5 kilometers per hour.

So this is one very basic description of one of the principles of the theories of relativity that we're discussing here.

The idea that if there's what's known as uniform motion between two objects, so when objects are moving relative to each other at a constant speed,

the choice of either reference frame is a valid one.

It's not wrong to say that from my perspective the Earth is moving backward at 5km an hour.

This is not an incorrect thing to say.

The idea that from my perspective the Earth is moving is not incorrect

But it seems slightly foreign to us

because we're normally used to using the Earth's reference frame as our go-to reference frame Now what we've talked about

so far are some of the similarities between both Galileo's and Einstein's theories of relativity Let's look at some of the differences.

In both cases we've seen that they deal with relative motion, but one place where they differ massively is the assumptions that they make to base their mathematics on.

Galileo's relativity is based on what we now call classical mechanics, which is the ideas of physics,

the ideas about the universe that seem very common sense to us.

They seem very logical to us.

For example, Galileo's theory of relativity makes the assumption that regardless of how fast, let's say, you are traveling relative to me,

we will both experience time in exactly the same way.

A second passing for me is the same thing as a second passing for you.

And why should we not assume this?

You know, that makes that makes quite a lot of sense to us if we're just using what's known as common sense.

The problem is the universe is a lot more complicated than this.

We'll come back to that in a second.

But just to clarify, Galilei's theory assumes the following.

Let's assume you and I are both stationary relative to each other, so we're just standing in the same spot and we're chatting, and we decide to do an experiment.

Let's say we decide to synchronize our watches so

that they read the exact same time to the nearest trillions of a second, because, you know, we've got the best watches available to us as created by modern technology.

So basically, our watches are reading the exact same time.

Now, let's say that you stay exactly where you are, and I start moving relative to you at, say, I don't know, five kilometers an hour once again.

Galileo's theory of relativity assumes that regardless of this relative motion between us, Our watches will read the exact same times and we will experience time in the exact same way.

So one second passing for you will be the same as one second passing for me.

This idea is known as universal time.

The idea that everybody in the universe, regardless of, you know, fast motion relative to something else or no motion relative to something else, experiences time in the exact same way.

And once again, our natural instinct is to think, well, yeah, of course that's true.

How is that not true?

In what universe is that not true?

Ours.

Now, before we get into this whole weird thing about time being experienced differently by us, let's look at these equations, which are known as the Galilean transformations.

Now, they look a bit hairy, but don't worry, we're going to get the gist of them, the basic ideas from these equations, if we just take a careful look at a couple of them.

First of all, where do these equations even come from?

What do all of these different quantities mean?

Well, you notice that in this set of equations, we've got values of x, y, z, and we've got x prime, y prime, and z prime, which kind of link back to the coordinate axes

that we chose for the two different reference frames that we were discussing earlier.

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Back then we were talking about the reference frame from the perspective of the earth, and the other reference frame was from the perspective of the person moving relative to the earth.

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And these transformations actually do exactly the same kind of thing.

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This is a transformation between two different reference frames where one

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is moving at a constant speed of V relative to the other.

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So specifically the idea is the following.

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Let's say the first reference frame, the reference frame that the observer, us, is in, has a coordinate system where, let's say, this is our origin, and we've got our x, y, and z axes.

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And the second reference frame is the one that we are watching as it moves.

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And specifically, it's moving, like I said, with a speed v, but it's moving in the x direction, the direction that we've called x.

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This means that for the moving reference frame, we can choose an origin.

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but that origin, the origin of the second reference frame, is moving relative to us because the second reference frame is moving relative to our reference frame.

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Now first things first, we're going to align the x, y, and z axes of our reference frame, we'll call our reference frame S, with the x prime, y prime,

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and z prime coordinate axes of the second reference frame, the one that's moving relative to ours.

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We'll call this reference frame S prime.

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The other thing that we see in the Galilean transformation equations is a quantity labeled T.

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This stands for time.

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And the convention that needs to be used in order for these equations to be true is

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that at a time of t is equal to zero, so we choose a random time in our reference frame as t is equal to zero,

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the origin of our reference frame is exactly at the same place as the origin of the moving reference frame.

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And crucially we can also say that t prime, the time experienced by a person in the moving reference frame, is also zero at this point in time.

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So basically we've coordinated our watches with somebody who is in the S' reference frame, so that when our watch reads t is equal to 0, their watch also reads t is equal to 0,

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and our origin is exactly in the same place as their origin.

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And then, as time progresses, their coordinate axes move to the right, move in the x direction, at a speed v.

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Now, let's deal with the Galilean transformation that says t is equal to t'.

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Basically, this is the one that's making the implicit assumption of universal time.

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This is the one that's saying time is experienced exactly the

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same by everyone regardless of how they're moving relative to each other.

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And because we set our watches so that t is equal to 0 aligned with t' is equal to 0, this means that if 5 seconds have passed in my reference frame,

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5 seconds have passed in the other reference frame.

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So time is not something to be worried about here.

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Time is experienced exactly in the same way by people in either reference frame.

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And we'll see that y is equal to y' and z is equal to z' as well.

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What this is telling us is that if we choose an object at a particular point in space, let's say this is our object,

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the y and z coordinates of that object are identical to the y' and z' coordinates of that object.

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What this means is a little bit complicated.

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Let's take a snapshot of our two reference frames, maybe two seconds after the origins of the two reference frames aligned.

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So t is equal to 2 seconds and t' is equal to 2 seconds.

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We know

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that at this time the distance between the origins of the two reference frames is equal to the speed with

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which reference frame s' is moving relative to s multiplied by the time.

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And if we say that the speed with

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which reference frame s' is moving relative to reference frame s is 5 meters per second, then we get

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that the distance between the origins of these two reference frames

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at a time of t is equal to 2 seconds is

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equal to 5 meters per second multiplied by 2 seconds

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because distance traveled is equal to speed multiplied by time

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so now at this particular moment in time from our reference frame

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and actually from the other one as well

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because times are identical in both of these reference frames the

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distance between the origins of the two reference frames is 10 meters

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and that distance is in the x direction or the x prime direction

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because remember the motion of the reference frame is only in the x or x prime direction.

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Now we've got this object in space.

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This has got nothing to do with what reference frames we have or what coordinate systems we're choosing.

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This is just an object here in space.

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It doesn't matter how we choose to describe it, but we can describe it in one of two ways in this particular case.

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Firstly, we can use the coordinate system of frame S.

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We can say that measured from the origin of the reference frame S, our reference frame, the object has coordinates of 4 meters, 3 meters and 2 meters.

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This means it's 4 meters to the right of the origin, 3 meters into the screen from the origin, and 2 meters above the origin.

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So what are the coordinates of this object in the reference frame S prime at this particular moment in time?

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Well because we've taken a snapshot we can calculate this easily.

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Now the origin that we're using is the origin of the reference frame S prime

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and we know that its X prime coordinate must be negative 6 meters

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because it's 6 meters to the left of the origin

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and it's still three meters into the screen from the origin

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and two meters above the origin and remember once again this is

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when we're talking about the origin of frame s prime and

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so we see

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that the x coordinate of our object is not the same as the x prime coordinate of our object

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but the y coordinate is the same as the y prime coordinate

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and the z coordinate is the same as the z prime

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coordinate this is done just to make life easier this is by construction we decided

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that our two reference frames would move only in the x

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or the x prime direction relative to each other and their coordinate axes aligned as well.

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This means that we isolate all of the motion into just one direction

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and we don't have to worry about the y or y prime directions nor the z or z prime directions.

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And so for this particular instant in time we can use the relationship between x

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and x prime coordinates for a particular object to give us the x prime coordinates of this object

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if we know what the x coordinate is.

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And if we don't even worry about taking a snapshot we can see

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that this relationship relationship between the X

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and the X' coordinates is directly related to the relative speed between the two reference frames.

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Because as time progresses, frame S' gets further and further to the right of the diagram as we've drawn it.

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This means that its X' coordinate is going to get more and more negative as time passes.

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But notice one other thing.

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The object's X coordinate stays exactly the same regardless of what time we're thinking about.

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Because this object is stationary in the reference frame S.

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It's not moving relative to the origin of the reference frame S or for that matter

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Relative to any point in our reference frame S and so

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that is a basic gist of the Galilean transformations Now

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if there's something that I haven't quite explained properly then let me know in the comments down below

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And I'll try and clarify a bit equally as always

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if I've made a mistake Let me know as well and I'll try and correct it as quickly as possible But anyway, so these Galilean transformations are based on very common sense ideas things

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that come naturally to us straight from childhood such as universal time.

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That's not even something

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that most of us would consider to question until somebody like Einstein came along and did it for us.

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In fact, I know speaking from personal experience, this is not even something I would have known was a thing that could be questioned.

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It's just that it's so ingrained into us from personal experience.

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So I guess the question is, why did Einstein question it?

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Why did Einstein think that universal time was something that needed to be trashed?

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Was he just a straight-up genius?

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Well, the answer to that, as we already know is yes he was, but there's a very specific reason why he questioned such ideas, and that reason is Maxwell's equations.

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Specifically, Maxwell's equations deal with electricity and magnetism, which means that they also deal with electromagnetic waves, light being one of them.

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Now if you haven't seen my videos on Maxwell's equations, check them out up here, I've made two of them so far and I've got two more left to come, and that will be in the new year.

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But the point is that Einstein started thinking about special relativity, the first theory of relativity he came up with because of Maxwell's equations.

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There was a weird mathematical artifact that popped out from the mathematics of Maxwell's equations when they were dealing with electromagnetic waves.

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These equations specifically said that the speed of electromagnetic waves must be constant.

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And they weren't talking about any particular reference frame in which this speed must be constant.

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They just said it was constant.

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And this was a really weird thing.

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Initially, people thought that Maxwell's equations would need to be modified to be corrected for this mistake.

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However, Einstein decided to include it in his mathematics and see where that took him.

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But it is a really strange idea.

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Let's say for example that I was to measure the speed of light and I found it to be whatever value.

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Let's call it C because that's usually what it's called anyway.

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It was a really weird thing for people to think that if I measured the speed of light to be C, then somebody who was moving, let's say, 10 meters per second in this direction relative to me,

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would also measure the speed of light to be C in their own reference frame.

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Because what this essentially meant was the following.

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No matter how fast you travel, you always measure the speed of light to be exactly the same from your point of view.

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And this is not how things normally behave, right?

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If you throw a ball at 10 meters per second, you're measuring its speed to be 10 meters per second.

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But then if you start running towards the ball at 2 meters per second, then from your perspective the ball is only moving away from you at 8 meters per second.

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Whereas with light you somehow couldn't catch up with it regardless of how fast you were moving, that was always the speed you measured it to be.

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But regardless Maxwell's equations popped out the fact that the speed of light must be constant regardless of reference frame.

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So this was the basic assumption that Einstein went by when he devised his theory of relativity or specifically special relativity.

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But then because the speed of light had to be constant in both of the reference frames that we're dealing with here, he had to let something else be flexible instead.

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He had to let the experience of time in each of these reference frames be slightly different, and the same is true for the experience of distance.

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This is why the effects of time dilation and length contraction are a thing.

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If you've never heard of these before, then I might make videos about this in the future, but there are already brilliant videos about this on YouTube, so check them out.

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I'll leave a link to some good ones in the description below if I remember to do it.

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But anyway, so one of the assumptions that Einstein made when talking about his theory of relativity

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was that the speed of light was constant in both of these reference frames, whether that was the one that was stationary relative to us

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or the one that was moving at 5 meters per second relative to us.

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And following all of this through mathematically, slightly changed the transformation equations that we saw earlier.

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These are the Galilean transformations and these are the ones devised by Einstein.

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Now we're not going to go through these ones in great detail, that I want to say for a future video, but if we look carefully, there is this factor of gamma.

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Now gamma is related to the relative speed between the two reference frames

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And this is what encodes for both length contraction and time dilation the difference in experience of time and distance

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Depending on what reference frame you're in now It's worth noting

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that there is a lot of experimental evidence for the universe to actually work the way

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that Einstein thought it did And not the way

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that Galileo thought it did So why is it

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so common sense for us to think of the universe in the same way that Galileo did?

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Well, it's because this factor of gamma does not become even noticeable

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unless we're talking about relative speeds close to the speed of light.

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And the speed of light is 300 million meters per second.

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And what this means is that for everyday velocities that we experience, let's say a bus is moving relative to us, or even a plane is moving relative to us,

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we don't have to experience these special relativistic effects.

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Because when the relative velocities of the two reference frames are small compared to the speed of light, and let's face it, even a plane is slow compared to the speed of light,

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the factor of gamma, like I said, is essentially negligible.

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And what we get are approximately Galileo's transformation equations.

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It's only in places like particle accelerators, or where things move very, very close to the speed of light, that we notice the special relativistic effects, the effects that Einstein predicted would happen.

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And that is why common sense, based on personal experience, tells us that universal time and other assumptions made by Galileo are actually true,

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when in reality, that's not the case at all.

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Now for me personally, this is a very good reminder

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that the universe is a lot more complicated than we realize and we should never take our common sense for granted.

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Of course, there's a reason why it's called common sense because it serves us very well in day-to-day activities.

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And even back in the day when our ancestors had to fight to survive, it would have helped them a lot.

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However, Einstein teaches us a very valuable lesson to question everything

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that we think is obvious and allow science to do its thing, test it experimentally until it's proven either incorrect and we need to find a new description

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or science tells us that it's quite likely to be correct.

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And with all of that being said, I think I'd like to end my discussion here.

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Thank you so much for watching.

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I've got a couple of updates for you.

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Firstly, like I said, this is my last video of 2019.

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And once again, I want to thank every single one of you for supporting me.

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All of you that have left nice comments, all of you that have subscribed to my channel, all of you that have left constructive criticism.

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I once again, can't thank you enough.

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I've got some exciting ideas for what I want to do with this channel for 2020

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so I'm looking forward to seeing you guys in the new decade.

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Secondly, I've also been thinking about starting a second channel because with this channel I keep it very physics focused.

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However, like you guys know, like many of you guys know, I've got a lot of extracurricular activities that I like to do in my spare time.

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Badminton, music, started getting more and more into video editing, color grading, so on and so forth.

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That's one of the interests that I've had as well.

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And I just generally like to have a chat about stuff, make it a bit more informal and just make videos

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that are a bit different to the physics stuff that I do on this channel.

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If you guys would be interested in seeing that then let me know

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and as always

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if you want a current place to see what I've been

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up to in my spare time then follow me on Instagram at Pluff Vlogs.

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I make vlogs on IGTV, well I've made one so far and I'm working on a second one but you know I do make vlogs there.

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Anyway thank you so much for watching and I'll see you in 2020.

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Bye!

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