Waching daily Feb 27 2018

What is mass?

This is a fundamental question,

which has recently, specially since the discovery of the Higgs boson five years ago,

has often come up in questions or discussions

on the IFT videos.

So I'm going to explain what mass is.

And...

this has to do with the Higgs boson in the sense that the Higgs fields in the vacuum

is the origin of the mass of particles with non-zero mass.

But let's cut the chase and let's find out what is mass.

To do that, we're using the scientific method,

which is as follows:

First, choose some concepts

which we consider fundamental,

and preferably defined in a practical way.

Next, study the relations among them,

both theoretically

and experimentally,

to reach our conclusions, if any.

And, if by doing more experiments,

we find that our conclusions are wrong,

we go back to point 1,

and start all over again.

Ok, let's choose two concepts that we consider fundamental:

space, which can be measured by distances,

in practice measured with my own ruler;

and time, which I can also measure with my watch.

If we now take an object

which is moving a given distance in a given time,

with no external forces,

we find that something, the quotient of distances and times,

which is the velocity, is constant.

Well, the velocity not only has a magnitude, which I call "v", but also a direction,

and is hence a vector, something that points in a certain direction.

So let's play a bit with vectors.

I should remind you about how to add up two vectors.

If I have a given velocity, which is a vector pointing in some direction,

and which I call "v1",

and a second velocity, which I call "v2",

the question is what is the sum of "v1" and "v2".

Easy! To add up,

we apply parallel transport to "v2"

until its tail is a the head of v1

and the vector from the tail of v1 to the head of v2

is the sum "v1" + "v2"

These are all the maths we need to go on.

Ok, next thing

is to do experiments in a billiard table.

An ideal billiard table, with perfect and frictionless surface,

with perfect balls, perfectly spherical,

as ideal as possible.

And then, two billiard champions are training by making pairs of balls collide;

each one smacks on a ball, and they check what happens after they collide.

These are vectors.

So the balls bounce back with velocities

in general different from the original ones, this with velocity v2'

(the ' meaning "after the collision)

and this with velocity v1'.

So what we find after many such experiments is the following:

the sum of v1 and v2

before the collision

equals the sum of v1 after the collision and v2 after the collision.

And this holds for any collision.

We also discover

that v1 squared + v2 squared

(these are numbers, so I can take their squares)

equals v1 squared after the collision

+v2', after the collision, squared.

Great! We're on a good track, we have discovered,

it seems, certains laws for collisions,

certain laws of nature in the dynamics of particles.

Let's now change things and perform the same experiment,

but with balls still of the same size, but made of different materials.

In such case, we immediatly find that these formulas are wrong.

To fix them, the most natural suggestion

is to associate a quantity, which I'm calling "m", to each of the two balls,

"m1" for the first, and "m2" for the second.

And we'll find, after much experimenting,

that the combination m1 v2 + m2 v2

is conserved.

And also here if we also add these two things, m1 and m2.

But this holds only for a given ratio of m1 and m2,

a certain ration is the only one such that these laws are valid.

Ok, we have then discovered two interesting things:

one is the conservation of momentum,

which for instance for particle 1 is m1 v1,

and second, the conservation of enegy,

the energy before and after is the same.

Note that the convention, for reasons having to do with other conventions,

such as what is a force and so on,

the formula for the energy we have discovered is 1/2 m v^2.

The enegry 1/2 m v^2

is a conserved quantity in particle collisions.

Ok, it seems we all should be happy that these laws work out.

But if we now do these experiments

with particles whose speed is not much smaller than the speed of light, called "c",

if their speeds are comparable with that of light,

then these conclusions are again wrong.

And the quantity m1 v1,

for the conclusion to hold,

must be divided by the square root

of 1 minus the particle velocity squared divided by the speed of light squared.

This formula must also be modified,

by replacing by c^2 here, removing the 1/2, and dividing by the same square root of 1-v^2/c^2.

Once we do that

the formulas for the conservation of energy and conservation of momentum are now correct.

In the meantime we have also discovered another fact.

I could rotate the billiard table without rotating the balls,

or rotate the balls without rotating the billiard table,

and independent of the orientation of this my reference system,

the laws are still the same.

Thus the basic laws of Mechanics are invariant under rotations.

One last point

Let me

take units in which the speed of light is 1.

Then using these formulas,

we find that, for a given particle, E^2-p^2=m^2

The energy and momentum depend on the velocity with respect to the observed, but the mass does not.

So energy and momentum are not relativistic invariants;

but the mass we have introduced here, which is the intertial mass, is a relativistic invariant.

When we introduce gravity and move on

to Einstein's Theory of General Relativity,

it turns out that the mass sourcing gravity is the same as this.

Inertial mass and gravitational mass are one and the same thing.

For more infomation >> What is mass and kinetic energy? - Duration: 9:20.

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Lexus IS 250 AUTOMAAT | Leder | Parelmoer wit | LM-velgen - Duration: 1:00.

For more infomation >> Lexus IS 250 AUTOMAAT | Leder | Parelmoer wit | LM-velgen - Duration: 1:00.

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Phu Quoc, Vietnam - Is It Better Than Phuket? - Duration: 5:04.

so I'm in Phu Quoc Vietnam and I'm on the beach really nice beach here only

small problem is you've got a lot of Vietnamese getting drunk at the moment

it's on a Sunday and it's their day off so it's kind of their only chance to get

drunk so it does get a little bit noisy at times anyway I want to answer the

question is phu Quoc better than Phuket I spend about 6 months of the year in

Phuket so I know it really well I've only been here about 3 days I was going

to come here last year and I read that it's a bit of a building site and it's a

bit boring so I didn't come and then this year I read a bit more I read some

things that said it was like paradise and it's the new Phuket so I thought I'd

come down here and just see which is I walked a lot a few kilometers all up and

down the different beaches and I got a motorbike out yesterday and I've got

that today as well and I did about 50 kilometers around the

island I will say the positives afterwards but I do want to talk about

the negatives first I think that they could make this a really good place it's

got loads of potential but they really are doing it wrong the first thing about

it is whereas in Phuket you can pretty much drive right around the edge of the

island and just look at the beaches you got some fantastic views as you go up

and down the hills you can actually see the beaches you can see the bays and

that's what I really like about Phuket but here you can't do that when you're

driving you can't see the sea the nearest it comes along this Beach which

is on the west is about 300 metres away from the sea so you have to keep going

down different places to try and see it and on the other side it's a few

kilometers from the sea so you've got to go down maybe three or four kilometres

down the road just to sea if the beach is good or not and you haven't got those

views the other thing they're building along the south part of the west coast

they're building these really big complexes and they're right next to the

sea and then they're blocked off so the actual beaches are public but you can't

get to them because they're blocked off by these different complexes that

they're building and they are just at the moment construction sites

especially where I'm staying you can't even really get to the beach the first

day I went down from where I'm staying to the road and then from the road

you've got all these hotels that kind of block the beach off so I went down one

and it says trespassers will be prosecuted

well the guard just kind of told me to go down there but it's not very good

it's kind of not easy the other thing is that there are a lot of places that

really haven't got character driving around the island there's actually

nothing on most of it so you're just driving along and you've

got fields either side there's a few cows occasionally but mostly it's just a

dual carriageway a few motorbike shops but no real character the only places I

saw with character were the port which looked quite busy and also the other

side of the river rather than the tourist market which is on the south of

the river it was quite good I drove the motorbike through the actual local

market and that was pretty interesting the place I would stay if you're gonna

stay here then I would stay near Rory's bar and sunset bar I think it's called

around that area and get a place near the beach then you can just really relax if

you want to relaxing holiday it's great you can just go to the beach and

then go back and then at night you can go to one of the bars on the beach so I

think that's fine and then if you want to go somewhere there are some islands

and I think you can get boats out to them you could also do some diving and

the other thing is to maybe walk around the port a little bit or go to the

market you could go to the night market which is on the south of the river or

you could go to the market that's the north of the river I didn't see many

foreigners there but it was more realistic it's the actual locals doing

the shopping so it's just more interesting for me I would say it's more

interesting rather than the tourist stuff so in general the positives I

would say is that if you want a quiet holiday and pretty nice beaches you want

to chill out then it is a place that you can come to I

probably would go to Thailand first but if you've been to Thailand a few times

then come here