General Relativity Question

Love it SG... lovely break down.

I think the biggest problem with the Twins Paradox is that two very different phenomena are being discussed and confused. We have inertial frame transformation laws and we have the observers' proper time. The real paradox is why does anyone think this is still a good scenario to discuss in the teaching of SR, other than after the teaching of proper time...What do you think?

Heh, heh, I would claim you are doing that here. You don't need to go into GR at all. Acceleration is handled perfectly well in SR... again, it's just a case of integrating up the respective proper times. At the end of the day, if your space-time is Weyl and Ricci flat then you are working in SR. Then again, it does depend somewhat on what you define as SR...

That predictable, huh

You keep asking me, and I keep forgetting to reply!And now I'm going to bed after seeing Kong for the second time... even better than the first time!So for now: Loop has some wonderful features but I still love the unification of everything (matter, space and forces) in SuperGravity, and by association String and M-theory. Loop still has a lot more work on the matter side of things.Off to bed...

Good answer. Be careful. It would be better to say that gravity IS the warping of space-time. The other fields then can act as sources for this warping. There is a big difference between the grav field and the other fields.Warning: advanced bit!!!!Mathematically, space-time is some manifold, M. Gravity is a connection on the tangent bundle. The other fields are connections on other bundles over M.In higher dimensional theories (Kaluza-Klein, SuperGravity, String, M-theory, etc), the idea is that you only have gravity*, but as you dimensionally reduce down to 4 dimensions, the higher dimensional gravity sectors are partitioned off and become the other fields.*well, maybe not quite as simple as this, but it will do for nowThis message has been edited by cavediver, 12-22-2005 05:30 AM

Unfortunately, that pretty much sums up your post.And you were doing so well earlier... No, this is not the analogy. This is a misrepresentation of the analogy. Things do not suddenly start rolling towards the depression. This relies on "gravity" to start the rolling! Depending on how you look at it, both bosons and fermions take up space, or neither take up space. Mass is not a function of taking up space. Bosons are both massless (photon, gluon) and massive (W, Z). More importantly, both bosons and fermions are described as fields. This makes no sense. No, I am talking about our ideas that cover the last 80 years. Hardly new. This is totally backwards I didn't even mention branes... they are irrelevant in what I am discussing. Planck's constant is not a distance, it is an action. There is the Planck length. I have no idea by what "takes up space" means.

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Thanks Iblis for your reply, i understand pretty much everything you wrote
  —Fabric wrote

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Oh dear...This message has been edited by cavediver, 12-23-2005 05:17 AM

Ok, let's try this...I will start with a classical field. Essentially a field is a value defined at each point in space and time. This can be a simple value, like temperature. So around the surface of the earth, each point has an air temperature. This is a field. Becaue the value at each point is a simple number, we call this a scalar field.Similarly, at each point there is a wind speed and direction. Now a speed and a direction is a vector, so wind is a vector field around the earth: at each point there are three numbers describing the vector.Another scalar field is air pressure. Interestingly, it is the differences in air pressure that give rise to the wind, so these two fields (wind vector and pressure scalar) are intimately related. BUT, it is local differences in air pressure that give rise to local wind conditions. There is no "action at a distance", just a long chain of pressure changes causing wind causing nearby pressure changes causing neaby wind causing further away pressure changes causing further away wind causing distant pressure changes... etc. You get the idea.Gravitation is very similar. There is a field throughout the universe, and at each point there are 10 numbers (so more complicated than a vector, this is a tensor) which describe how far away are neighbouring points. This field is called the metric, as it is how measurements are made up.If you want to find the distance between two distant points, you add up (integrate) all of the metric distances between the infinitessimally close points that make up the jouney from your starting point to your end point. Critically, this includes distances in time as well as space.What we think of as everyday normal space, is just space with no curvature: the metric distances are the same in all directions at all points. This is flat space(and time). When the numbers change, the distances change, and we get curvature.Just as with the wind and air pressure, curvature at one point will cause curvature at a nearby point (to keep things consistent) and this will cause curvature at a further away point, etc, etc.Objects travel through space-time in straight lines at constant speed. If space becomes curved, we travel along the straighest line possible... this makes us think there is a "force" called gravity pulling us in strange directions. This is just us trying to follow our straight paths.If you think that there are times you are not moving at all, you are are simply moving purely in the time direction. If we add a nearby planet, it causes changes to metric next to it, which causes changes further out, which causes changes all the way out to where you are. Your straight line pointing straight up through time gets bent by the changed metric and now points slightly towards the planet (but still predominantly up through time), and you see this as a motion towards the planet. But there is no force. You were always moving, it is just the direction that has slightly changed.Ok, this has gone a bit too far into GR. We are talking about fields. Remember, a field is simply a number (or set of numbers) at each point of space(and time). There are rules as to what values these numbers can take. Einstein's Equation is the set of rules for the metric field, Maxwell's Equations are the rules for the classical electromagnetic field. Wind and air pressure have their own set of meteorological rules.Think over this, and if you are happy let me know, and I will continue into quantum fields which is where your question really lay anyway.

So, just the simple stuff then?

Good reply.But not stupid. You've just digested too many dubious layman accounts and need something a little meatier. Have you tried Brian Greene's book? Try that and then maybe Hawking's Universe in a Nutshell. The best place to get a good grounding though is John Baez's site and the physics FAQ he hosts hereAbsolutely. There is no simultaneity in relativity. The "order" of events that are not causally related themselves has no meaning. If I clap my hands on the earth, and an astronaut claps his gloves on the moon within a second of each other, there is no concept of who clapped first. The order of the events purely depends upon vantage point. There is no correct answer. If the astronaut is orbiting alpha Centauri, then it is anything within 4.3 years of each other!! Well, I know what you mean. It is a fundemental property of the universe and not just a measurement problem. BUT the light time is intimately related to this property and is equally a fundemental property. Exactly... In the same way the universe guarentees that angles in triangles add up to 180 (in flat space) It is "simple" geometry within the mathematics of relativity. This catching up is simply your observation of someone else's time. This observation is very dependent upon your motion, especially whether you are moving away from them or moving towards them.Your own passage of time is a measure of "proper time" which we just integrate up over your journey which depends upon your acceleration. You would get less of an effect, becasue you would be travelling slower on average (as slow acceleration/deceleration implies spending more time proportionally at slow speeds) But there would be no qualitative difference.

Absolutely. What you are calling simultaneous is just what we conventionally call "faster than light". Yep, the telepathic messages will sometimes be in reverse, so that one twin perceives the other as travelling backwards against the flow of time. Such is the price of breaking causality with telepathy (or any other FTL mechanism). Another observer will be able to see one twin receive the message before he sees the other send it! In an extreme case, he could see the message receieved and still have time to intercept the first twin to stop her sending it! I would put it the other way round. If you want to preserve causality, you have to give up simultaneity. This applies to telepathy, hyperspace, warp drive, sub-space transmissions, etc, etc. This is why wormholes are also time machines...

Well, local causality is fundemental to sensible dynamic quantum field theory so we probably wouldn't exist without it! But non-local causality breaches shouldn't be too much of a problem.However, GR does not allow for multiple time-lines. There is one past, one future, and they are set in stone. Consistency is the name of the game. The observer could not stop the twin from transmitting, having seen the reception, because it did not happen. In this case his freewill (should any exist) is removed.You can postulate the ability to "change" the past, but you are moving outside of GR. And as it is GR that has actually allowed you to break causality, you are off into fairy-land...

As Fabric was asking about fields, I thought I'd link this thread to a brief primer I made on quantum fields over in the Coffee House. If anyone wants to go further, or ask any questions, just drop in a post.My decription of classical fields is here Message 28The quantum field stuff is here: Message 90