h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

That may be a far bigger question than you realise... how long do you have?

I'll answer at the most basic level, anything more would require me to go do a lot of reading to brush up on the subject.

So here's the basic thing.

Spacetime is any model where the three dimensions of space are put together with the fourth dimension of time. If I remember correctly there isn't actually one thing called spacetime, but rather several of the blighters each helping to model different things. Gravity is possibly a product of spacetime (with spacetime being a taut rubber sheet and the mass being a bowling ball which causes smaller nearby objects to fall towards it. But each of those objects has their own spacetime with its own rubber sheet in which they are the bowling ball. Or something. It's complicated.)

It's what we had before Hammer-time

Methinks I'm agonna get shot down again but still...
Specifically true or not, this gave me a handle on a few things when I was rather younger:

In a sense, space and time are one and the same ...
Generally, space is thought of in miles or kilometers etc, however

It takes (about) 8 minutes for sunlight to reach us so there's 8 minutes of space between (is that rather easier to grasp than saying 93,000,000 miles?).

To the edge of the (known) Universe? about 13,000,000,000 light years at present* - easier to grasp than, all those (groups of 3) zeros of miles? You're welcome to work it out - or play with
http://htwins.net/scale2/

Yes/No?

A83646291

* (according to one estimate - that may well be rather small)

People used to think of space and time as different things. Space had 3 dimensions and was measured in distance, while time had only one dimension, we progress through it, and it is measured in seconds, days etc.

Then Einstein discovered that speed behaves strangely. If Joe is travelling along a railway line at 20 mph relative to Mike who is standing on the platform, and Joe sees a train in front of him moving away from him at 20 mph, then Mike won't see this train travelling at 40mph, but at slightly less than that. And the faster they're going, the more these discrepancies occur.

The whole business of motion and time was much more complicated than people had thought.

Then someone developed a form of four dimensional geometry which treated space as three of the four dimensions and time as the fourth one. In this geometry, Einstein's odd results could be easily modelled by just rotating objects in this four-d world. They came up with the name "space-time" to describe it.

It is a more accurate way of describing the world than treating space and time as separate things, but even space-time isn't necessarily the "true picture", as some mathematicians have used up to 11 dimensional "spaces" to give even more accurate predictions.

"Then someone developed a form of four dimensional geometry which treated space as three of the four dimensions and time as the fourth one."

That would be Hermann Minkowski in 1907, two years after Einstein developed special relativity.

"...some mathematicians have used up to 11 dimensional "spaces" to give even more accurate predictions."

I assume you're thinking of M-theory here, in which case it hasn't made any predictions that we can use to decide if it's more accurate than general relativity. That could change in the future though.

Well how one can visualise space time-like a 2-D rubber sheet or what?

The rubber sheet thing is a picture of general relativity, an extremely accurate model of spacetime (going by how well its predictions fit observations). The idea is that the mass of objects distorts spacetime, like putting something on a rubber sheet would, and then things follow geodesic paths (a geodesic is the "straightest" line you can get on a curved surface - eg a great circle on a sphere). Thus gravity is not actually an attractive force, but a result of the distortion.

Also bear in mind that objects don't exactly move in spacetime, rather they have a worldline made up of every point they occupy during their existence, so rather than rolling a ball on your rubber sheet, you should take a piece of chalk and draw a line.

I got your point. But is space time two dimensional or 3 dim. or 4?how many dimensions space time has?

In gen rel, it has four - three spacelike and one timelike. As Gnomon alluded to, string theory and M-theory require more dimensions with some of them (all but four) so small we don't notice them (like a cylinder could be so thin it looks one-dimensionsal).

Off the top of my head which might be erroneous, the speed of light (m/s) multiplied by time (s) scales as distance (m = m/s x s). So adding an additional axis, c.t, which is time scaled as distance, to the normal three distance dimensions of space, creates a four dimensional graph upon which one can represent objects and events in "space-time".

The advantage of this is in the way one can use this to better "visualise" the different viewpoints different observers have of the same events but in different "inertial frames", which are represented as changes in the axes used.

So earth is bending space time like from all points on its surface? Will this be true ?

The whole mass of the planet bends spacetime, not just the surface.

Yeah ok! But does that mass bends the space time in
All directions not just downwards?

Yes!

To qualify the last answer the Earth is a sphere (more or less) which exerts a gravitational force acting perpendicular to its surface. An object passing over the pole will experience the same force changing its trajectory as one passing by any other point of the globe such as the equator or Biggleswade.

I'm not going to get into Frame Drag as it complicates things more than a Menagé a Trois.

t.

Unfortunately, to visualise a bending of four-dimensional space-time, you may need to think in 5 dimensions!

I only do that on wibble and thing!!

t.

Now! its becoming complicated. So what will be the 5th dimension?
Can we think of that physically?how the motion of a particle is effected in that dimension?

When physicists start talking about multiple dimension then one must be careful not to get too carried away with thinking about Star Trek or Doctor Who. Sadly the concepts are rather more boring than that.

Consider what quantum theory actually developed from. It came from (amongst other things) trying to explain the origins and energies of a bunch of lines visualised when one zapped electricity through an elemental gas. Atomic emission spectra.

The main lines can be explained through use of normal 3D space treating the nucleus of the atom as a point charge and then the electrons as standing waves using cunning spherical mathematics developed in the 18th century.
Electron positions can then be described using either 3D coordinates or more usefully by three 'quantum numbers' (called n, l and m).

n is fundamental energy of the electron level and is an integer 1,2,3, 4 etc.

l is called the 'angular quantum number' which can go from 0 to n-1 in integers (so for n = 2 it can be 0 or +1)
It describes the shape of the 'wavefunction' in which the electron exists.

m is called the magnetic quantum number and describes the orientation in space of each wavefunction (often called the electron orbital - but is important to remember that other particles can have wavefunctions too). m is any integer between -l and +l (i.e. for l=1 it can be -1, 0 and +1).

These 'quantum numbers' are actually just constants you plug into the Schroedinger equation that describe everything about an electrons behaviour in orbit about a nucleus.

Transitions between the different orbital energy levels give rise to energy emitted when the movement is downward and so you see this as photons corresponding to the energy of the lines seen in the emission spectrum


So these three quantum numbers are the 3 'dimensions' in the Schroedinger equation.

But.... things get more complicated.

People noticed 'fine structure' in the spectral lines under high magnification - especially visible when electric or magnetic fields were applied across the discharge tube generating the spectrum.

To explain fine structure a new quantum number or 'dimension' in the equation became necessary.

s came from looking at this fine structure or 'line splitting' in the spectral lines.
It is often called (poorly) 'spin' and is a magnetic moment of electrons. It can have the value +1/2 or -1/2


Under even higher magnification you get 'hyperfine splitting' which occurs with nuclei that also possess a 'spin' (called nuclear spin)
So the nuclear spin also needs a new quantum number or 'dimension' to describe the overall energetic state of an atom.


Finally when you look at spectra from even more energetic discharges (this is what they do in particle accelerators) you split atoms and see spectra associated with energy release from high energy fundamental particles. Again these particles have properties that give rise to other spectral lines that require further 'dimensions' in mathematical formulae used to calculate the energy states describing the lines seen.

It started to get boring to keep calling them another form of 'spin' and so with quarks you start to see the physicists get silly and calling the new states - 'colour', 'beauty', 'strangeness' etc.

_These_ are the things that get called extra 'dimensions' in string theory equations and the like and are best not thought of as extra dimensions as in having a parallel universe where Spok is a ruthless dictator or where Rose has never met the Doctor.
The reality is far more boring, but does make the science seem 'sexier' to those who get lost in the jargon or (almost) mythology associated with fundamental particle physics.


(You can of course have time dependence in quantum equations - that is more of a dimension in that sense - but aqain, mathematically it's just another variable in the equation).