The Theory of Relativity

[HoloYolo]

Alright, so I've got a few questions about this theory.

1. What does it mean by space "contracting", and time dialates?

2. How come the speed of light is always "c"?

3. How are space and time the same thing?

4. How come it affects everything BUT gravity?

Thank you fellow smart people,

Kaboom!

[Kertherina]

1. What does it mean by space "contracting", and time dialates?

2. How come the speed of light is always "c"?

3. How are space and time the same thing?

4. How come it affects everything BUT gravity?

1. Space contracts as in it gets shorter in the direction you are travelling (Lorentz contraction). This is closely related to time dilation, which is the phenomenon that time goes slower the faster you go.

Why both of these things? They are direct logical consequences required for consistency with c being constant in every frame of reference.

If something like a train is moving near the speed of light, and it emits a beam of light, then it has to travel with the speed of light for both observers outside standing still, and for observers on the train. If time and space would not change, then from the observer on the train the beam of light would travel at c but for an outside observer it would be faster than c. This can't happen. So, time goes slower the faster you go, or in other words an outside observer will see time pass more slowly for the train. Now, since time passes more slowly, that means the light is travelling more slowly too and thus not faster than light any more.

As for the lorentz contractions, someone less tired than me can probably explain that.

2. That is a good question. Historically, it was acknowledged that c has to be constant in all frames of reference for maxwell's equations to not break down. Special relativity is then a direct consequence of this, accessible via thought experiments only. As for why exactly is c always c in every frame of reference - why is any physical law just the way it is? It's a question that has no answer.

3. Well they are not exactly the same (otherwise why would we have different names?), but they are part of the same: space-time. Every bending of space results in a bending of time and vice versa, they interact like one entity.

This also has implications for velocities. In fact, you are always moving at the speed of light - but through space-time. If you don't move in space, you move in time with c. It's a 4D-velocity vector in space-time. This also explains why the faster you move through space, the slower time passes because a larger portion of c is going in spacial velocity, rather than in time.

4. What do you mean "it"? And in fact, gravity also has effects on time (and obviously space). This is the field of general relativity though, whereas until now it was all special relativity. Special relativity is the "easy" part, concerning itself with non-accelerating objects not in gravitational fields that is accessible via thought experiments alone. General relativity is, as the name suggests, more general, and much much more complicated.

[K^2]

As for why exactly is c always c in every frame of reference - why is any physical law just the way it is? It's a question that has no answer.

Nah, we can do better than that. I mean, sure, ultimately, any science question will run into an unanswered, or indeed, unanswerable why question. But the point is to take it a few layers deeper every time.

First of all, the speed of light is just a conversion constant. It's how many meters there are in a second. This has no reason to change any more than there should ever be a different number of feet in a mile. So the more correct way to state the question is why it's the fastest speed there is and why light travels at that speed regardless of frame of reference.

And the real answer to this is that everything travels at the speed of light all the time. Or more precisely, 4-velocity always has magnitude c. Stationary things propagate purely in the time direction, and so they appear stationary. Things that cut at a bit of an angle appear to move, as they are in a different place in space at a later moment in time. The angle at which something propagates through space and time is determined by momentum and energy. And the relationship between momentum and energy determines mass. Hence more massive objects require more energy and momentum to be accelerated.

Light is massless, and so it has a linear relationship between energy and momentum, E = pc. That means that light always cuts at a 45° angle, always traveling same amount through space and time. Change of coordinate system changes energy and momentum, but preserves linear relationship. So you get light that's red or blue shifted, but still traveling at c.

This brings up the question of a) Why is light massless? and Why does relationship between energy and momentum is what we call mass? Unfortunately, this is starting to get complicated. The answers to both of these questions come from Quantum Field Theory. Light is massless because Higgs Mechanism allows for a single massless electroweak boson, and that's light. Behavior of mass as actual mass has to do with mass shell and a singularity in the propagators, and that's getting really complicated.

The ultimate answer to all of the thread questions, as far as we know, is "Because Lagrangian is invariant under a continuous group of local transformations which includes Poincare subgroup." That actually gives you the entirety of General Relativity as a consequence. But it's turtles all the way down from there.

[PB666]

Nah, we can do better than that...... from there.

The simpler answer would be "42".

[K^2]

I was thinking that very thing, especially near the end there. In the sense of needing to understand the question to have any chance of making use of an answer. Hence, "The ultimate answer." But I find that sometimes knowing some of the answers before you can ask the question helps find the right way.

[lajoswinkler]

Alright, so I've got a few questions about this theory.

1. What does it mean by space "contracting", and time dialates?

2. How come the speed of light is always "c"?

3. How are space and time the same thing?

4. How come it affects everything BUT gravity?

Thank you fellow smart people,

Kaboom!

You should specify which one you're talking about in the title. There are two theories of relativity. Special and general one.

[wumpus]

You should specify which one you're talking about in the title. There are two theories of relativity. Special and general one.

1. Space "contracting". Depends if you are asking about special or general relativity. In special relativity, space only contracts from the point of view of an observer moving at relativistic speeds. The general theory explains why the planet Mecury measurably processes (the Aposis and Perapsis rotate around the Sun). The gravitational field of the Sun is contracting space enough around it enough that the circumferous around the Sun near Mercury divided by its diameter isn't pi.

2. It just is (or as Newton would say, "I fain no hypothesis"). Relativity tends to hang on the idea that C is somehow the definition of time, and that this is fundamental to the universe. Einstein appeared to believe that since the the speed of light could be derived from the Maxwell Equations without requring a reference state, so should C. Michealson and Morely essentially answerd an old [but a hundred years after M&M] Steven Wright joke "if you are going the speed of light and turned your headlight on, what would happen" to point out that no matter how fast you go (it would take Einstein to show that accelerating an object with mass to C was impossible), you always measure light moving at C with respect to you (by experimental result. They did the obvious check of measuring the speed of light in two seperate directions and got *zero* movement, when the Earth was "obviously" moving much faster just going around the Sun.

3. They aren't. Entropy doesn't change with distance.

4. I don't get this one at all. PS: Special reletivity (that doesn't bother with gravity and accleration) is wildly easier and requires only algebra. Bringing gravity into the mix requires general relativity and is beyond my pay grade. I still suspect the question doesn't make sense.

edit: I remember reading a book by Albert Einstein himself called: "Relativity, an easy explanation anyone can understand". I'm almost sure it existed, but Amazon isn't helpful. It did explain Special relativity down to Jr. High level (but probably included some algebra), but had to handwave really hard on the general side of things (it didn't go into tensor calculus).

Edited March 15, 2015 by wumpus

[PB666]

I was thinking that very thing, especially near the end there. In the sense of needing to understand the question to have any chance of making use of an answer. Hence, "The ultimate answer." But I find that sometimes knowing some of the answers before you can ask the question helps find the right way.

You did a pretty good job anyway. Science is not knowledge, but a process of discovery that relies heavily on and sometimes stumbles over past knowledge. To facilitate the process it is better not to lead the discovery with facts that maybe overstated cases.

Gravities future:

1. Do gravitons exist?

2. How many variants of Higgs and how do they affect gravity?

3. If we knew exactly how gravities force is constituted we could calculate the constant to comparable Planck's precision (and in doing so also calculate the mass-energy equivalent for nearby celestial objects to very precise levels).

[Sillychris]

Alright, so I've got a few questions about this theory.

1. What does it mean by space "contracting", and time dialates?

2. How come the speed of light is always "c"?

3. How are space and time the same thing?

4. How come it affects everything BUT gravity?

Thank you fellow smart people,

Kaboom!

Kaboom, I am going to try to answer your questions succinctly, but in a different order.

3) Space and time are both dimension in our four dimensional universe. You are usually moving through this universe in some combination of a high speed along the time axis and a low speed along the 3 spatial dimensions. It turns out that if you treat time as a dimension, stick the appropriate constants in front, and add it quadrature to your 3 spatial dimensions like you would for any vector sum... everything's speed through spacetime is the same. If you move faster through space then your travel through time slows down to accommodate and vice versa. The relationships are obviously not linear but this is a good way of verbalizing it.

2) This one defies logic for low-speed, low energy, mass based critters like us. It turns out that if you have no rest mass, the rules are different. Actually, they aren't. All the relativistic effects fall out at low velocities. At speeds closer to c, the universe preserves the cosmic speed limit in different reference frames. This means that if we are flying towards eachother at 0.6 C, we won't see the other ship approaching at 1.2C. Velocity transformations from SR prevent that and we end up seeing the other ship approach at a subluminal velocity.

Light is just a special case of these maths where it has no rest mass and subsequently sits on the light speed asymptote.

1) Once you accept that space-time is four dimensional and light moves at C for any reference frame, the consequences of time dilation and length contraction fall out quite naturally in order to preserve these relationships.

4) We don't understand gravity. Sorry.

[K^2]

1. Do gravitons exist?

Gravitons only make sense in quantized gravity. The full problem is not quantizable, but you can do mean field theory of gravity (which works above Plank Scale and does not work bellow it) and it will give you gravitons and their description as quantum particles. If you are working with pure gravity, however, quantization isn't useful. So then you just treat it as fields and forget about particle properties.

2. How many variants of Higgs and how do they affect gravity?

Higgs mechanism only provides for single Higgs field, and it's sufficient to describe our observations. It is an SU(2) field, which has 3 generators. I suppose, you can think of it as 3 particles. But that's like saying that there are 8 different gluons. Without symmetry breaking, as there is with U(1)xSU(2) of electroweak, they are all the same. There could be more Higgs-like fields, of course, but there is neither need nor evidence of them in current model.

Higgs field does not couple with gravity directly. So the only effect is via the masses of electroweak bosons, which we already have accounted for.

3. If we knew exactly how gravities force is constituted we could calculate the constant to comparable Planck's precision.

Non sequitur. Gravity's coupling constant is a free parameter of the theory, just like every other coupling constant. It cannot be computed from any other coupling constants or parameters. The exact knowledge of how gravity works (which we have) will not help us do the actual computations. There are experiments we can do in regimes where gravity starts coupling to other forces, which is how we normally measure coupling constants, but the energy levels required are much above these we have access to. The fact that gravity is so many orders of magnitude weaker than electromagnetic forces makes probing gravitational constant in direct ways impossible with our technology. And various indirect methods only yield the precision we get.

[MircoMars]

Hi, I also have some questions about relativity and time dilation. how much time differential is there between the planets of our solar system? I mean mercury is deep in the gravity well of the sun and moves quite fast, neptun is far out and moves slower. how do i calculate this and what do i need to take into consideration?

[K^2]

Hi, I also have some questions about relativity and time dilation. how much time differential is there between the planets of our solar system? I mean mercury is deep in the gravity well of the sun and moves quite fast, neptun is far out and moves slower. how do i calculate this and what do i need to take into consideration?

Time dilations due to gravity and orbital motion are multiplicative. Orbital dilation is given by sqrt(1-v²/c²). Gravitational by sqrt(1-2GM/(rc²)). Here, G is gravitational constant, M is mass of the Sun, c is speed of light, v is orbital velocity, and r is the distance from Sun's center. For a roughly circular orbit, this simplifies to approximately sqrt(1-GM/(ac²)) * sqrt(1-2GM/(ac²)), where a is the semi-major axis. But this doesn't account for dilation due to planet's gravity. For planetary bodies, this is roughly multiplicative as well. So time dilation factor for the planet is approximately given by the following.

t_planet = t_{deep space} * sqrt(1-GM/(ac²)) * sqrt(1-2GM/(ac²)) * sqrt(1-2Gm/(Rc²))

Where m is mass of the planet and R is its radius. You can compare these factors between different planets to figure out the difference in time flow between different ones.

[PB666]

Gravity's coupling constant is a free parameter of the theory, just like every other coupling constant. It cannot be computed from any other coupling constants or parameters.

It may be 'a free parameter of the theory' but it is not free of the interactions that give rise too gravity, if you know precisely how many moles of something is in a given space, say a carbon-12 diamond, then you know just about everything, then you should be able to predict the gravitational attraction between two carbon-12-diamonds to the relative accuracy of knowing how many molecules of C-12 exist in each diamond. You are going to have to give this argument up, the proof of the pudding is in the eating, as long as gravity cannot be defined precisely (and there are ongoing arguments in the literature about what is causing variation in very cold effects), then there is not perfect understanding of how it works.