SCIENCE (said in a deep, meaningfully spooky voice)

[Polito45]

Or, Tinlad's ponderings on the meaning of life, the universe and everything.

The story so far:

Soopytwist started it by posting this -

If you want to visualize how big a Minecraft world is...



This is taken from the extraordinary Scale of the Universe 2 by Cary and Michael Huang, here: http://htwins.net/scale2/

That image makes no sense.
Neptune is bigger than Sirius B?

Wow it really is.
I find that 10^7.6 more interesting than the Minecraft bit.

What I can't quite get my head around is the absolutely enormous size of VY Canis Majoris compared to our own sun! Kind of puts you in your place doesn't it?

That is a very cool site.
Yeah, I remember seeing an image a few years ago that showed the sun and then sequentially bigger and bigger named stars.
It changes your perspective on the universe that such truly massive stars exist.

I was reading last night that to make our star - the sun into a black hole you would to shrink its radius from the 450,000 miles that it is
down to less than 2 miles, keeping its mass the same of course.
Apparently the dark star (black hole) at the centre of our galaxy is 2.5 million times the mass of our sun.

Mass is weird. The star Sirius B is roughly the same size in volume as Earth but it's mass is near equal to our Sun! So it's both smaller than our sun and as big at the same time!

This happens at the other extreme end of the scale too. Quarks, the building blocks of Protons and Neutrons are smaller than the particles they make up but their mass is greater! Strange Quarks are smaller than Up Quarks but are 50 times as massive.

Stars, planets, atoms, protons and quarks - all very similar wouldn't you say? Boy it's tough being an atheist.

There came the sound of heavy boots stomping down the hallway, the door flew open and -

Quarks, the building blocks of Protons and Neutrons are smaller than the particles they make up but their mass is greater!

Wrong.

EDIT:
I should probably elaborate slightly. The mass of a neutron is about 940 MeV, and it's made up of one up and two down quarks, the masses of which are 2.3 and 4.8 MeV respectively. However, the gluon field associated associated with each quark is considerably more massive (but still not greater than that of a neutron or proton). It's this gluon field that binds the quarks together into a particle (strong nuclear force). For further reading see: mass-energy equivalence and binding energy.

Also, this...

Mass is weird. The star Sirius B is roughly the same size in volume as Earth but it's mass is near equal to our Sun! So it's both smaller than our sun and as big at the same time!

... is not really that weird. A grapefruit and a shot put are about the same size, but have very different masses. It's called 'density'. Sirius B is smaller than the Sun, but as massive. It's the same size as Earth, but more massive. "It's both smaller than our sun and as big at the same time" is just... wrong.

You've awakened the physicist.

...the gluon field associated associated with each quark is considerably more massive...

I thought the force carrying particles didn't have any mass?
Photon, Gluon, (shit, can't remember what the weak force particle's called - is it weak gauge boson?) & Graviton.

What I found myself doing the other night (I have insomnia) was trying to imagine a dark star in all 4 dimensions.
You know the way you always see one graphically represented in 2D as a funnel with an event horizon around the upper part of the funnel
and a singularity where the funnel reaches a point at its base?

In truth of course it exists in all 4 dimensions just like any other star, but it gives off no light.
And, it's mass is so great that if you were to station yourself close to it's event horizon and look back at another ship at some distance away
you would see them moving unnaturally quickly, just as they would see you moving unnaturally slowly.
But to each of you time would appear to be moving normally. That to me is one of the hardest things to get your head around -
How can mass grip and warp time?

Too much science...I'm out.

EDIT

Not yet.

How can mass grip and warp time?

That'll be Quantum Foam, the fabric of space time. The more mass an object has the more it distorts space time - hence the warping of time and the gravitational pull of an event horizon....I think. Sheldon Cooper, help me out here!

Now I'm out.

I thought the force carrying particles didn't have any mass?

The photon doesn't. The gluon (probably) doesn't. The W and Z bosons do.

But despite (probably) not having mass, the energy of the force the gluon mediates (the strong nuclear force) results in the mass of the hadrons they create being higher than just the sum of the quarks. This is mass-energy equivalence: E = mc^2 in action!

How can mass grip and warp time?

That'll be Quantum Foam, the fabric of space time.

Quantum foam is a theory concerning the nature of spacetime at the planck scale, primarily regarding the creation of virtual particles out of vacuum energy. It has little to do with general relativity.

There are hand-wavy explanations of why gravity distorts time (typically involving bowling balls on rubber sheets), but they typically aren't very satisfactory... and are often misleading. A proper explanation is a little bit more involved, but if you really want to know, I can do my best...

... but it probably belongs in a different thread.

/off-topic

Isn't Quantum foam from String theory? It sets a limit on how small things can be - around the Planck length - both matter & time.
Which smooths out the quantum foam and allows for a joining of quantum theory and general relativity?

Anyway, yes. Please have a go at explaining how mass warps time.

[Tinlad]

Hurrah! A chance to get properly nerdy.

OK, I'll start with the quantum foam thing, to get it out the way. It's not from string theory - it's a hypothesis based on what the Heisenberg uncertainty principle says might happen when you look at spacetime on very small scales. In fact, the smallest scale there is: the Planck length, which is of the order 10e-35 metres. This is unfathomably tiny. That's 100000000000000000000 times smaller than a proton.

Energy is directly interchangeable with mass, and vice versa. That's what E = mc^2 means. The entire universe is filled with energy - even 'empty' space. A bizarre consequence of this is that, at any given time, some of that energy can transform into mass: particles can be formed out of empty space. In order that this doesn't violate various conservation laws, particles are formed in pairs: one particles and one anti-particle. These then exist for a fraction of a second before annihilating with each other (the mass turns back into energy).

When you start doing the maths for very small distances and times, it turns out that the mass of the pairs of particles that get created can be quite high. And, as we know from general relativity, mass bends spacetime. So it's hypothesised that if you look at spacetime at this really really small scale, it's not smooth: it's all bumpy and distorted because of all the particle pairs that are popping in and out of existence. This is the 'quantum foam'.

Next up: gravitational time dilation! I bet you can all hardly wait.

[Savara]

What I always thought was cool was when you have pairs of particles forming near a black hole, and then one particle being sucked into the black hole and the other not, so they don't annihilate.

[RB]

I wonder if this is the right thread to put forth my theory of the quantum cow?

Maybe later.

[Polito45]

Yes, I think I understand or at least can comprehend the idea of quantum foam.
A huge amount of energy being converted into a tiny amount of mass and vice versa via E = mc^2.

What I was thinking earlier was - imagine you're sitting in your lounge.
The spacial dimensions in the room have a fine grid like structure which you can see.
Ignoring the mass of the earth (it's a very, very big room and happens to be in deep space).
You can see that the grid is misshapen around the objects in the room, just by a tiny but observable amount.
This is the effect that the mass of each object is having on the spacial dimensions around it.

Now we introduce a bowling ball. It's suspended from the centre of the ceiling by a thick thread and hangs in mid-air.
It has the most mass proportionally for its size than anything else in the room.
The grid lines that represent the flow of the spacial dimensions are observably warped around it.

You put your right eye as close to the bowling ball as you can.
In theory this means that time is moving more slowly on the surface of your right eye than it is on say... the hairs on your arse.

I can see how if the spacial dimensions are suffused with some kind of a field then the mass of the object is affecting the particles that make up the field and so appear to be warping the spacial dimensions, but time doesn't have a field, does it? So how can mass affect it?

I know Einstein said that the spacial dimensions and the time dimension were intimately entwined and should be thought of as one structure - spacetime.
I just have a hard time (no pun intended) getting my head around how mass can warp something that apparently isn't a something.

[Tinlad]

It is a tricky thing to get your head around - but hopefully the way I'll explain it will show why it has to be the case.

I'll have to do it in a few steps though.

Part I: The equivalence principle.
Take a sealed box, and build your physics laboratory inside it.

Experiment 1: you put your laboratory on the surface of the Earth, where the gravity is g = 9.8 m/s^2. You perform experiments (of any kind) in your laboratory and record the results.

Experiment 2: you put your laboratory in a rocket, take it to outer space, and turn on the engines such that you're accelerating at 9.8 m/s^2. You perform the same experiments and record the results.

The equivalence principle says that the results you get for 1 and 2 will be identical. Similarly:

Experiment 3: you hoist your lab up on the air and drop it, so that it's free-falling towards the Earth at 9.8 m/s^2. You do your experiments whilst in free-fall.

Experiment 4: you take your lab to outer space, and stop. You do your experiments in the weightless environment.

Again, the equivalence principle says that the results you get for 3 and 4 will be identical. Free-fall is indistinguishable from weightlessness.

Part II will use this to show that light must be affected by gravity.
Part III will then explain why this leads to the time dilation.

[Mr.Clark]

I can see how if the spacial dimensions are suffused with some kind of a field then the mass of the object is affecting the particles that make up the field and so appear to be warping the spacial dimensions, but time doesn't have a field, does it? So how can mass affect it?

I know Einstein said that the spacial dimensions and the time dimension were intimately entwined and should be thought of as one structure - spacetime.
I just have a hard time (no pun intended) getting my head around how mass can warp something that apparently isn't a something.

You're still thinking space and time are separate, but as you said, they're actually just one thing - spacetime. So if something warps space, by definition, it's also warping time.

What I always thought was cool was when you have pairs of particles forming near a black hole, and then one particle being sucked into the black hole and the other not, so they don't annihilate.

1) Is that Hawking radiation?

2) How does that not violate the conservation of energy? Where does the energy of the second particle go?

[Tinlad]

Part IIa: Gravity and light
Now we set up a different experiment.

We have two people, Alice and Bob. Alice is in a transparent BoxLab™, free-falling towards Earth (starting from 100 m up, for example). Bob is an observer on the surface of the Earth.

Alice performs an experiment. See mounts a laser beam 1 m above the floor of her lab, and fires it at the opposite wall of the laboratory. The equivalence principle says that being in free-fall is indistinguishable from being in a zero-G environment, and so she sees the laser beam travel in a straight line across the lab and hit the wall 1 m above the floor.

Bob, however, sees the laser being fired from 100 m above the surface, but then sees the laser hit the opposite wall of the lab some tiny fraction of a metre lower (relative to the surface of the Earth); i.e. the laser beam is falling towards the Earth at the same rate as the laboratory.

The lab is falling towards the ground at a rate g, and the photons that make up the laser beam are falling at rate g. Light falls towards the ground at the same rate as everything else!

[Jezreel]

[RB]

But depending on Bob's position, shouldn't he either see the beam hit slightly higher due to the photons having to travel further to him and thus he sees into the lab wall's past when it was higher above the earth or see some kind of odd Doppler affected light pastern on the wall?

[Tinlad]

No: the laser will always hit the same point on the wall, regardless of the observer. Otherwise you could have a light-sensitive switch mounted on the wall that would be activated or not depending on where you observed it from. There will be a slight doppler effect, but that's irrelevant.

You could replace the laser with a gun. For Alice, the bullet travels in a perfectly straight line (as though in zero-G). For Bob, it curves downwards, falling at the same rate as the laboratory. The same applies for light.

[Tinlad]

Part IIb: Paradox, holy crap!
Imagine we've got two machines. The first takes an apple, and converts it to energy in the form of a beam of light. The second takes the beam of light, and converts the energy into mass... in the form of an apple. This is totally allowed because of mass-energy equivalence: E = mc^2.

We put the first machine on the ground, and the second one 100 m up in the air. We feed an apple into the bottom machine, it gets converted to a beam of light, which the second machine receives and turns into an apple.

This apple then falls 100 m... back into the first machine. Great, an endless apple cycle.

But what if we put a waterwheel type contraption underneath the falling apple? We can get energy out of the falling apple, for free! The world energy crisis is solved, Nobel prize, etc.

No. The Universe (unfortunately) doesn't like perpetual motion machines.

The reason this doesn't work is that the beam of light loses energy as it moves upwards through a gravitational field.

We're nearly at time dilation, I promise.

[Jezreel]

Tinlad is awesum.

[Polito45]

Yes, I get it. The light beam appears to be traveling in a straight line to Alice but that's because
she's falling towards the earth at exactly the same rate as the transparent BoxLab™ and the light beam.

Bob sees the light beam as being curved downwards because it is. It's being drawn down a gravity well towards the earth,
as is Alice and the Boxlab. It's a matter of perspective.

Gravity is the warping of space by mass. And accelerated motion is indistinguishable from gravity.

Does this mean that, you know when you put a guy in a high-G spinning contraption, spin him up till his face goes funny.
Stand around and have a laugh. - If you had to go and live on a planet with the same gravity you'd be walking around with that face all the time?
How are you going to find someone to have sex with you when you look like that?

[RB]

What I don't get is how the light can curve inside the falling lab regardless of observer viewpoint unless gravity is affecting the photons differently to how it is affecting the walls.

I roughly get relativity in broad terms. I get that if you are in a car and throw a ball backwards at the same speed as the car is travelling forward then to you the ball flies away from you but to someone stood by the road the ball drops straight down but this falling lab one seems wrong in my mind unless the light falls faster than the lab is falling.