Questions about E=mc², universe shape, expansion and gravity waves

[GBR]

Homework Statement

After todays exams, I'm having a few well deserved beers with a friend. We are pondering about some things we're not competent enough to comprehend (I'm a journalist and he is an architect).

1. e = m*c² -- how does lightspeed come into this equation, and why is it squared?

2. Shape of the universe: How can something have a shape if it does not occupy a tangible space? For example, if we live in a saddle shaped universe, how can we say it it is saddle shaped without any observers who are able to see it as so?

3. Expansion: Can gravity have an influence between parallel universes, and can it explain expansion and dark matter (ie. our universe is getting stretched by other universes in our neighborhood)?

4. Gravity waves: What if we don't find 'em?

The Attempt at a Solution

Beer talk.

(sorry if this is considered spam and drunken physics posting is a faux pas)

 

[kreil]

You've posted this in the wrong forum, as this clearly isn't a homework question. Nevertheless, you've got my attention:

1. This webpage has a very readable derivation with only light maths:

http://www.adamauton.com/warp/emc2.html

2. From what I understand, the shape of the universe was determined by a simple observation made by Edwin Hubble: He noticed that stars/galaxies that were farther away from the Earth were moving away faster than those nearby. (He knew they were moving away because of red-shifted light due to the doppler effect). Moreover, he noticed that this expansion speed was constant at a fixed distance no matter which way he looked in the sky.

The natural conclusion to draw from this is that the universe is spherically shaped and is expanding (imagine a balloon, where the surface expands quicker and quicker as it gets larger)

3. Parallel universes are still just a theory, and although we know how gravity *works* we don't know what it actually *is*. Connecting the two using present theories would be an excellent exercise in futility.

4. Hopefully we just find the graviton. I'm almost positive it is predicted by String Theory, so finding it would provide the first tangible evidence that the theory is more than just theoretical hot air.

 

[zhermes]

Far from a faux pax, drunken physical questions are perhaps the best and most fruitful.

1. e = m*c² -- how does lightspeed come into this equation, and why is it squared?

c squared is just a proportionality constant here---it converts between our conventional units of mass, to our conventional units of energy. There are lots of other ways of explaining the presence of $$c^2$$, but I think this is perfectly sufficient for your question.

2. Shape of the universe: How can something have a shape if it does not occupy a tangible space? For example, if we live in a saddle shaped universe, how can we say it it is saddle shaped without any observers who are able to see it as so?

Shape doesn't just tell you how something looks from the outside; it also tells you how things behave in that environment. Try drawing a triangle on the surface of a sphere, hopefully you can convince yourself that the sum of the angles is actually larger than 180 degrees. There are other configurations where the angle would be less. In either case, this has an effect even to an observer existing within that geometry. Another example would be walking along a mobius strip---coming back to where you started.

3. Expansion: Can gravity have an influence between parallel universes, and can it explain expansion and dark matter (ie. our universe is getting stretched by other universes in our neighborhood)?

No. Parallel universes cannot (for the most part) interact with our universe---thats what makes them different universes. Note also that dark energy is the one that has to do with accelerated expansion.

4. Gravity waves: What if we don't find 'em?

That's really really unlikely... If you ask most astrophysicists they'll tell you we've already observed gravitational radiation (see: http://en.wikipedia.org/wiki/PSR_B1913+16), but only indirectly. BUT, if we were to NEVER directly detect GW... i suppose it would completely change our notion of how gravity works---most notably, we'd have to throw lots of general relativity to the wind.

 

[Quinzio]

Homework Statement

After todays exams, I'm having a few well deserved beers with a friend.

Usually men in front of a beer talk about women... :)

We are pondering about some things we're not competent enough to comprehend (I'm a journalist and he is an architect).

You're interested in science. That's important.

1. e = m*c² -- how does lightspeed come into this equation, and why is it squared?

Can't quite answer you, but dimensional analisys says it's coherent.
From motion laws E=F*s= m*a*s = [kg] [m^2] / [s^2].
So there must be a speed squared in the equation.

2. Shape of the universe: How can something have a shape if it does not occupy a tangible space? For example, if we live in a saddle shaped universe, how can we say it it is saddle shaped without any observers who are able to see it as so?

More than the shape we can measure curvature. If everywhere there is e.g. a constant positive curvature you can say you live in a spherical universe.
But you can't say you live on a shere. The shape of an object has sense only seen from a higher dimensions world, e.g. 4th dimensions for us.

3. Expansion: Can gravity have an influence between parallel universes, and can it explain expansion and dark matter (ie. our universe is getting stretched by other universes in our neighborhood)?

N.A.

4. Gravity waves: What if we don't find 'em?

N.A.

The Attempt at a Solution

Beer talk.

Have fun.

(sorry if this is considered spam and drunken physics posting is a faux pas)