[ukmicky]

quote:  Oh, sorry, I just looked back on page 1 of this thread and realised what you were referring to.

Me too[:I]



Michael                 HAPPY NEW YEAR                    

[madmortigan]

Hi there

Just went through the discussion quickly, so I may have missed something.

One main problem I see with the reasoning is the attempt to apply special relativity to a problem that includes non-inertial systems of reference.

The twins paradox is only brought up in text books to demonstrate the weirdness of relativity, when compared to newtonian mechanics. However, it can't bedescribed fully in the scope of general relativity. The key point is that the astronaut twin leaves the earth - ie, accelerates to a speed, travels for so long, then comes back, etc. This is not an inertial reference system.

If you don't take into acount accelerations, you end up with a very symmetrical situation. The astronaut twin travels at a certain speed with respect to the earth twin. But, the same goes for the earth twin (ok, take him of the earth, and put him on a space station). He also travels with the same certain speed (opposite direction) with respect to the astronaut.

The difference between the two is that the twin who leaves earth accelerates to a certain speed, etc. as I said earlier.

Don't ask me to describe what's up in the twins paradox in term of general relativity!!

[madmortigan]

Hi there

Just went through the discussion quickly, so I may have missed something.

One main problem I see with the reasoning is the attempt to apply special relativity to a problem that includes non-inertial systems of reference.

The twins paradox is only brought up in text books to demonstrate the weirdness of relativity, when compared to newtonian mechanics. However, it can't bedescribed fully in the scope of general relativity. The key point is that the astronaut twin leaves the earth - ie, accelerates to a speed, travels for so long, then comes back, etc. This is not an inertial reference system.

If you don't take into acount accelerations, you end up with a very symmetrical situation. The astronaut twin travels at a certain speed with respect to the earth twin. But, the same goes for the earth twin (ok, take him of the earth, and put him on a space station). He also travels with the same certain speed (opposite direction) with respect to the astronaut.

The difference between the two is that the twin who leaves earth accelerates to a certain speed, etc. as I said earlier.

Don't ask me to describe what's up in the twins paradox in term of general relativity!!

[Rincewind (OP)]

Can anyone tell me what branch of physics or what version of relativity the interval equation comes from?  The one Solvay said: I = x2 + y2 + z2 - t2 (we should have superscript on a science forum really)

Cos if I is invariable then that basically says what I was saying at the start, and it excludes the twins paradox (as I understand it).


I don't really know the differences between special and general.  I thought special was wrong because Einstein had invented a constant to make the results fit the static universe model. If this is true what's the point of special since general came along?

(guessing from madmortigans post - general takes into account acceleration while special just talks about relative velocities, but please expand and/or correct that guess)

[madmortigan]

General relativity describes accelerating reference frames. Its math is hard. Special relativity is much easier and can be done with college level math. Thus I strongly suggest getting a textbook and solving all the problems - shouldn't take long. Popular science - although quite fascinating, doesn't give enough hard facts for anyone who feels curious about stuff.

Tha famous constant for anti-gravity was invented by Einstein in the scope of general relativity, right before Hubble poseted his findings on galaxies moving away from each other, thus suggesting an expanding universe.  

I'll go back to check that equation, but I've got to go now, need to file my tax return (speaking of relativity and the lot!)

go with the force!

[Solvay_1927]

Andrew,
the invariant spacetime interval I = x^2 + y^2 + z^2 - (ct)^2 comes from relativity - I think it's specifically from the attempts (by Minkowski?) to give a geometrical interpretation to relativity.  And note that it applies to special as well as general relativity.

MadMort's right that the only difference between special and general is that the former (1905) only applied to inertial (uniform constant motion or rest) frames of reference, whereas the latter (1914/15) extended that to non-inertial (accelerating) ones.  The special theory is just a "special case" of the general one - it's not wrong, it's just "incomplete".

The "cosmological constant" that you're getting confused about is a "fudge" that Einstein put into his general relativity formula to ensure that the universe was static.  He later said that this was his "greatest blunder" because his theory (without including this "fudge" constant) predicted that the universe was expanding.  So if he'd left the constant out and said "I predict the universe must be expanding", he'd be looking very smug when Hubble confirmed this prediction in the late 1920s.

Hope that helps.
Paul.

[Rincewind (OP)]

Cheers geez, that's brilliant:)  

You know, when there's something you should know and should have known a long time ago, but have only just found out?  Like a fog lifting, nice one:)

[Rincewind (OP)]

Dya see what the equatino means, yeah?  If you reduce the three spatial dimensions to a resultant distance s, you get I = s^2 - ct^2... hang on, where'd that c come from?  Musta missed that the first time round, What does that mean?

I'll get back to you

[Rincewind (OP)]

the distance two events are from each other, minus the distance light has travelled in the time between these events, is invariant.  

Hmm, must sleep, but thanx for clearing up the relativities for me.

[allmee]

The peaple on the space ship would percive a diferance to the peaple on the earth but the ship wood be in red fase going awaiy and blue fase coming back so were is the time diferance.
sorry for the speeling, Half a bottle of op rum

[Solvay_1927]

Andrew - I think that's a fair way of describing it, yes.

Allmee - you really were p*ssed, weren't you!  (I can't say you've inspired me with the confidence to invest in your perpetual motion machine, though. [])

[Rincewind (OP)]

So it's kind of like the pythagoras triangle, except it's kind of got two hypotenueses and only one regular side (or three regular sides and two hypoteneuses if you take the three spatial dimensions as three dimensions); that is the area of the square of one side (the distance) minus the area of the square of either of the other two sides (the distance light has travelled, and the interval) leaves the area of the square of the remaining side.

Interesting concept.