Originally Posted by
Mayflow
I would like just a basic description of what GR and SR are about and what they are useful for, for us.
Ok, fair enough, let's see what I can do.
SR is quite simply a model that tells us how, disregarding any effects of gravity, measurements of space and time are related between observers in relative motion, and also how space is related to time and vice versa. It tells us that lengths and clock readings are not absolute, but rather relative to some point of reference; for example, if you stand still and a clock passes by you at a very high speed, you will see this clock go slower as compared to a clock that is stationary with you. Likewise, if you see a ruler pass you by at a very high speed, you will see this ruler to be shorter in the direction of travel as compared to a ruler stationary with you. SR as a mathematical model tells us exactly how the measurements in the two frames are related; this relationship is not arbitrary, but instead works in just such a way that it leaves the laws of physics unchanged. In other words - SR ensures that the laws of physics are the same for all ( inertial ) observers. If you measure the speed of light here in a lab, you get exactly
c. If you measure it in a spacecraft moving at relativistic speeds, you also get exactly
c. If you turn on the TV in your living room it works just the same as it would if you were in a fast moving rocket. And so on. The laws of physics are the same for everyone, and in order for this to be possible, motion trades space for time and time for space, leaving the separation between physical events unchanged, and hence the laws of physics invariant. There is no local experiment you can perform that would tell you if you are in uniform motion or not
unless you have an outside point of reference - precisely because everyone experiences the same physics, so there is no intrinsic difference between a frame in motion and one at rest, all that can change is the relationship between frames in space-time.
So once you cut out all the complicated thought experiments and mathematics and philosophical arguments, the basic notion behind SR is really very simple - it ensures that there is only
one set of laws of physics which is valid for all observers, regardless of their state of ( uniform ) relative motion. Your toaster works on earth just as well as it does if you were in a fast moving rocket, because it is subject to the same laws of physics. SR can also be somewhat generalised to include any arbitrarily accelerated motion; what we find then however is that the beautiful symmetry of inertial frames is no longer there, and the relationship between observers becomes more complicated, both conceptually and mathematically.
SR does a good job in modelling the relationship between any observers in otherwise empty space; where it fails is in cases where
gravity becomes relevant. For example, if you have an observer very very far out in empty space, and an observer somewhere very close to a massive object such as the Sun, then SR still works fine
locally at the locations of each observer, but it no longer works if we try to relate these two frames to one another, over an extended region with a gravitational field in it. And this is where GR comes in - it allows us to relate measurements between observers at different points in the vicinity of sources of gravity. These sources can be mass ( planets, stars etc ), but also less tangible things such as very strong electromagnetic fields. It tells us how test particles behave over time when in a region with gravitational sources, and it therefore provides a model for gravity itself. Unlike in the old Newtonian mechanics which uses forces, the formalism used by GR is a purely geometric one - it tells us how measurements of space and time are affected by sources of energy-momentum. The basic result is that once such sources are present, then lines which ran parallel very far away cannot remain parallel as they approach the gravitational source - not as the result of any forces, but because the geometry of space and time itself is affected. This works a little like longitudinal lines on the surface of the earth - they are parallel at the equator, but as you go north ( or south ) they slowly approach, and eventually meet at the poles; not because of forces, but because of the geometry of the earth's surface. Same with gravity - the world lines of massive particles approach as they age into the future, because space-time between them is no longer flat, but curved, just like the earth's surface is curved.
The main consequence of GR is that concepts of space and time are valid only locally, and specific to each observer. This is best demonstrated with a concrete example - consider a black hole ( or any other small body ) with a mass equivalent to that of the Sun. We have two astronauts in a rocket very far away from the body, and they draw a map of what they see outside their window. For that purpose they draw concentric spheres at equal intervals around the central body : r=1km, r=2km, r=3km... and so on. It is not hard to see that for such far-away astronauts, the spheres at r=4km and r=5km from the central mass are exactly 1km apart. Now one of the astronauts wants to check whether this is actually true, so he jumps into a shuttle and proceeds to the sphere at r=5km; he leaves a small probe at this point that continuously fires a thruster so that it remains stationary there. He attaches a cable to the probe, and then allow himself to freely fall downwards, towards the next sphere at r=4km. How much cable will be needed ? When he was far away these two spheres where only 1km apart - but now he finds that he falls and falls and more and more cable is being unspooled, and in fact it takes
1723km of physical cable to reach the previously mapped r=4km sphere ! So somehow what is 1km from the point of view of someone very far away suddenly becomes 1723km for someone who is actually there and travels from r=5km to r=4km. Ditto for clock measurements. That is the meaning of curvature - that measurements of space and time are not absolute and universal, but depend on where you are. They are local notions, and
not shared by all observers; you cannot apply the far-away notions of time and space to the physics close to the body and expect everything to work out fine. This relationship between measurements at different points and times is gravity, and is modelled as being the result of curvature of space-time - GR tells us how exactly this geometry is related to sources of energy-momentum.
So - SR gives relationships between observers in otherwise empty space; GR gives relationships between observers anywhere, including in regions with sources of gravity. In both cases the relationship works in just such a way that everyone sees the same local laws of physics - SR formulates the laws in a form that does not change when observers move, and GR formulates them in a form that does not change when gravity is present. It turns out that SR and GR are actually the
same model - SR is merely a special case of GR for scenarios where there is no curvature, i.e. in flat space-time.
As for actual applications, I give you two examples - the electrons in old cathode ray tube TVs move at relativistic speeds, so without accounting for the laws of relativity, these old-style TVs quite simply would not work. Another very concrete example is that without the laws of relativity, gold would actually have a dull silvery colour - this is due to relativistic effects in the quantum mechanics of the electron orbitals in gold atoms and molecules ( the details are pretty complicated, but you get the idea ).
Hopefully this makes a little sense. I won't be writing any more at this point, but rather leave you to ask specific questions if you have them. You might also be interested in reading up how all of this came to be, and you will find that relativity arose not as an isolated and purely theoretical idea, but rather as an attempt to explain concrete and empirical observations, mainly about electromagnetism and light. See here :
History of special relativity - Wikipedia, the free encyclopedia
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