Gravitational Force!

All matter has a wave function associated with it, it's just that it's only really significant for photons and is less evident even for electrons. As the limit of propagation of a wave is c, this limits the ultimate spatial, and indeed time dimentional velocity of all matter.

Thinking that a body has a space-time velocity with constant magnitude c, which has components in both time and space, you can then say that for the body at rest, its velocity is a maximum c purely in time - v[t] = c; v[x] = 0. As soon as you introduce a component of velocity in space (v[x]) you can see that the component in time must be reduced by using pythagoras.

So v[t]^2 + v[x]^2 = c^2.

And v[t] = sqrt [c^2 - v[x]^2]

Then the time dilation is given by v[t]/c = sqrt[1 - v[x]^2/c^2]

Quite a nice analogy.

Where's the panadol...

This makes for some really interesting thinking. I'm just here on a flying visit right now, so I can't contribute much at the moment...

Seani.

It might be easier to think of gravity as an effect of the mass of the Sun and Earth. Mass distorts space and time (like two hippos in a bed-they tend to roll towards each other, not because they like each other but because the mattress is distorted by their mass. It is the mattress that causes them to pull together, not each other. Take away one hippo and the other one will probably fall out of the bed (i.e. the Earth would head off in a tangent from its orbit)
Gravitional waves to my limited knowledge have yet to be detected. Gravitons, virtual particles that interact with mass are another idea, but particles with mass cannot travel at or above C (speed of light).
Another thought, if gravity can only interact at C then the size of the universe cannot be any bigger than (age of universe x C).

Another thought, if gravity can only interact at C then the size of the universe cannot be any bigger than (age of universe x C).

Thats would only possibly give you the observable universe. There a bits of the universe that are not connected to other bits (light can never have passed from one to another) so the universe would be bigger still.

If we go with age X c, then the radius of the universe should be about 14 billion light years across. This also though assumes that the geometry is flat. At cosmological scales spacetime is curved so the 14 billion ly radius is too small. (This can apparently be shown by general relativity but my grasp of the argument is tenuous).

What really bugs me about this is that when we see a deep field picture and we are told that some galaxy or other is say 10 billion light years away. Since the universe is 14 (ish) billion years old then you'd think that the galaxy must have formed in 4 billion years. But not so. Its another reason why the idea of a light year is a bit meaningless at these scales.

According to arxiv.org/abs/astro-ph/0310233 the universe is at least 78 billion light years in diameter.

Al = so the visible universe is 14b ly but the whole universe (including the bits we can never hope to see) is 78b ly? Am I reading that right?

I ask because I read a couple of years back something similar but I had forgotten what the size was for teh whole universe.

Cheers

Dave

Al = so the visible universe is 14b ly but the whole universe (including the bits we can never hope to see) is 78b ly? Am I reading that right?

Not quite; the universe expands. Say a photon that left a galaxy when it was first created and reaches us now. The galaxy that the photon came from is around 50 billion light years away now. So the observable universe has a radius of around 50 billion light years.

78b ly is just a lower bound on the whole universe. So its probably a lot bigger.

Cheers,
~Al

edit: www.sciam.com/article.cfm?articleID=0009...Number=5&catID=2
46 billion light years apparently.