Tell us what you know about the theory of RELATIVITY without using anything but your own brain.

Mundane Pointless Stuff I Must Share (MPSIMS)
#1

The word relativity is in all caps in the thread title because I began a similar thread hereabouts on the theory of evolution a while back, and I don’t want the two threads confused. The other thread was in Great Debates; I’ve opened this one here because, while I fully expected a fight to break out on evolution, I tend to think the ToR is a mite less controversial. I could be wrong, of course. I’ve been wrong seven times since breakfast.

That said, the basic idea behind the threads is the same. Here’s the rules:

#2

Okily dokily.

Special relativity:

  • All movement is relative; there are no special or privileged frames of reference nor any true state of being at rest
  • The speed of light is always constant, regardless of reference frame
  • The consequence of these is that differences in relative speed lead to time, length, and mass dilation via the Lorentz equation, which I have since forgotten.

General relativity:

  • Gravitation and acceleration are equivalent,
  • Gravity is a geometric property of spacetime
#3

I could fill considerably more than a post, so let’s just cover the basics.

First of all, there are two different theories of relativity (well, three, if you count Galileo’s, but that’s not too revolutionary): Special relativity and general relativity.

Special relativity (henceforth, SR) derives from a pair of axioms: First, that the laws of physics are exactly the same in all inertial reference frames (this assumption dates back to Galileo), and second, that there exists a speed called c such that an object moving at that speed would be observed to move at the same speed from any reference frame (light appears to be an example of something that moves at this speed, but that’s not fundamental to the theory). This second axiom was rather thoroughly demonstrated by Michelson and Morley in 1904, but can also be inferred from Maxwell’s equations (Einstein seems to have been ignorant of the Michelson-Morley experiment at the time he developed the theory).

The core concept of SR which derives from these axioms is that time and space are two different manifestations of a single four-dimensional spacetime. A change of velocity in space is equivalent to a sort of rotation in this four-dimensional spacetime. Just as a rotation in three-dimensional space can result in a change in the width or height of an object, so too can a change in speed result in changes to individual coordinates of a measurement in spacetime (notably time dilation and length contraction). While relativity is often discussed in terms of these changes in coordinates, it’s much easier to work in terms of the invariant quantities which are inherently associated with the phenomena being measured. For instance, in the three-dimensional analogue, while the width, depth, and height of a rod will depend on the way it’s oriented, if you take the width squared plus the depth squared plus the height squared, you’ll always get the same value, the square of the actual length of the rod. Likewise, in spacetime, if you take the square of the spatial part of the distance between two events, and subtract the square of the time difference between the events, you’ll always get the same result, the square of what’s referred to as the “proper length” or “proper distance” between the two events.

Another consequence of the interrelationship between space and time is that the momentum and energy of an object increase more quickly with speed than would be predicted by Newton’s theory. Although this is sometimes interpreted as an increase in an object’s mass when it moves at great speed, it is simpler and more convenient to interpret it as a change in the formulas for momentum and energy, such that the depend on a quantity called proper velocity, related to proper length, rather than to the ordinary velocity. No real-world object can have a velocity greater than c, nor can any object with nonzero mass ever have a velocity equal to c, since such an object would have infinite or imaginary energy and momentum, but there is no bound to how high proper velocities can get. Proper velocity, denoted by u, is related to regular velocity, denoted v, by the formula u = 1/(sqrt(1-v^2/c^2)) * v, which is sometimes written as u = gamma * v. The correct formula for momentum is then P = mu, rather than P = mv, but the difference is not noticeable at small speeds because at such speeds gamma is very close to 1. Likewise, the correct formula for the total energy of an object is E = gammamc^2. Notably, this means that even an object at rest (where gamma = 1) still has considerable energy; this is not noticed in Newtonian physics because total energies do not matter in Newton’s theories, only changes in energies.

This post is getting long enough, so I’ll stop there, and come back to general relativity a bit later.

#4

A quick list of things that pop into my head:
[ul]
[li]Matter and energy are equivalent.[/li][li]Mass warps space.[/li][li]It’s impossible to determine if two events are simultaneous.[/li][li]From my point of view, time flows slowly for moving objects.[/li][li]From my point of view, moving objects are compressed in the direction of motion.[/li][li]From my point of view, moving objects gain in mass.[/li][li]From the point of view of the moving object, all these things could be said about me.[/li][li]Nothing can travel faster than the speed of light in a vacuum.[/li][li]Time flows slowly in accelerated frames, no matter what the source of acceleration.[/li][/ul]

#5

Um… there’s general and special relativity. I forget which is which.

One of them involves gravity warping time and space. The other has to do with light.

Look, on a good day I really do remember what relativity means. Today is not a good day.

#6

D’ok, I think I can take a crack at this. IANAPhysicist, merely a layman, so please be kind!

Special Relativity:

  1. Time is not absolute, and events will appear different depending on the location and acceleration of every observer relative to the event.

  2. Given two objects moving in relation to each other, no one can say which one is the one actually moving. Unless one undergoes acceleration (inertia), then they are both on equal footing.

  3. Matter and Energy are two sides of the same thing. (E=MC2) Matter can be converted into pure energy. The equation “Energy = Mass * the Speed of Light, squared” tells us how much energy would be brought forth from any given amount of mass. The purest way to achieve this is combining matter with anti-matter.

  4. Time and Space are two sides of the same thing. You can imagine it as any body is always moving through space or time at the speed of light. When you are standing still (not moving through space), you’re moving through time at the speed of light ©. However, the faster you accelerate through space, you start trading off your speed through time, and your clock will start to slow down relative to any clock that is not accelerating through space. So…

  5. The faster something accelerates, the slower their clocks tick when compared to anything that’s not accelerating with them. This is known as the Time Dilation effect. The faster you accelerate, the more you dilate along the direction of travel, the slower your clock ticks, and the more mass you gain (according to any outside observer; however, to you things seem perfectly normal and it’s the outside that’s shrinking and slowing down). This is why you cannot travel faster than the speed of light, because that’s the point where you reach infinite mass, therefore it would take infinite energy to accelerate you any further. You would also breech your own light-cone.

  6. The points above also explain why light always appears to travel at C relative to you, no matter how fast you are going. The Dilation effect always perfectly balances out your observation of massless waves/particles like light/photons.
    General Relativity:

  7. Gravity is a force that warps spacetime. Therefore, anything moving through spacetime will take a curved path if there is gravity present. If the gravity is strong enough (so that the the mass is so compressed beyond its Schwarzchild Radius), it can curve spacetime so much as to cause a gravitational singularity, where all paths beyond the event horizon of the singularity cannot escape, whether light or matter. This is called a Black Hole.

  8. There appears to be no difference between gravity and acceleration.

  9. If an object is in a gravity field, it can be said to be undergoing acceleration, and if you accelerate you will feel the the same inertial effects of being in a gravity field of similar acceleration (in the line of direction).

I’m sure there’s a bit more to it, but thats all that comes to mind so far. Sheew

#7

E=mc[sup]2[/sup]

You asked. :slight_smile:

#8

All things are relative
All relatives are things
My relatives took all of my things.

What did I win?

Unclviny

#9

Relativity, the short version, is that as the velocity of stuff* gets very very close to c, the speed of light, the Newtonian version of physics falls to pieces and things get strange.

First, one must understand the concept of “reference frame”
Your reference frame, as you are sitting here reading this, includes you, the computer, the chair you are sitting in, and all other objects at rest around you.
If you are standing on the sidewalk, a passing, moving bus and it’s passengers will be a reference frame of its own – from the point of reference of the passengers on the bus, they are at rest and the surroundings are moving past them. Reference frame is also called ones “rest frame”.
IMPORTANT: There is no supreme or “correct” rest frame. Everything is relative, literally.
Got all that?

Other concepts that I’ll breeze over:
Time dilation: moving clocks run slower then a stationary clock in the stationary clock’s rest frame – this gets noticeable at velocities close to and at the speed of light.

Lorentz contractions: moving stuff is shorter then stationary stuff in the stationary stuffs rest frame – again, noticeable at velocities close to and at the speed of light

Also, there are things like rest mass and gamma and Einstein’s equation (E=mc^2), and all of those put together can be used to edit Newton’s equations so that they are relativistically correct. We usually don’t bother editing them unless the velocities we are dealing with are very close to c, however. In our regular everyday world, Newton’s equations are still a very good approximation for how the world works – but they don’t tell the whole story.

*stuff being anything – mostly we’re talking about electro-magnetic waves/particles, which all move at speed c in a vacuum
** I am a physicist. Ok, Physicist in Training. P.I.T, if you will.

#10

Special relativity is the more general framework of the laws of motion that recreates Newton’s laws at low velocities, but also accounts for any speeds, including those near c, the speed of light.

In SR, time is not a parameter but its own separate component like the 3 components of space. It works the same way, but with a factor of -c. This framework makes it so SR will work in any coordinate system or reference frame.

In order for this to be true, it means that measured lengths and time intervals will depend on relative motion. One can measure the proper length of something in its own rest frame, and measure a completely different length for it in a frame where it is moving. Similarly, one can measure a proper time interval for the object at rest, which will be different for someone in motion with respect to the object.

SR says that an object going less than c will always go less than c, no matter what frame of reference you’re in. It also says that an object going at c will always go at c and never be able to slow down or speed up. It also says that anything going faster than c will always go faster, but so far there doesn’t appear to be any physical example of this.

General relativity is the theory of mass and spacetime. It’s based on the equivalence principle, the postulate that an accelerating frame and a frame in a gravitational field are indistinguishable. Starting from there with some simple thought experiments, one can see that both acceleration and gravity cause time to flow at different rates at different positions, and can cause light to bend, phenomena not found in Newtonian gravity.

The main equation is the Einstein field equation, which tells how mass density induces curvature. Solutions to the Einstein equation are different metrics, which describe line elements in spacetime that depend on what kind of mass distribution there is. Sources of curvature are described by the stress energy tensor, which shows that not only does mass/energy cause curvature, but momentum density induces curvature, meaning that motion itself can warp spacetime.

This is all of course just made up by scientists who like to sit around and think up cool sounding ideas for fun but have no basis in reality. These so called relativists think they know everything, but they haven’t shown how the universe began, so really, the whole theory falls apart.

#11

Although Einstein published the paper with E=mc^2 at the same time as his paper on special relativity, I don’t think E=mc^2 is considered part of the theory of relativity. It’s interesting that Einstein is best known for that equation and the theory of relativity, but they’re completely different concepts.

#12

Well, it’s necessary to define relativistic mass in both forms of Relativity. As such, I thought one probably led to the other… Either thinking about the consequences led to Special Relativity, or needing a way to conserve mass in Special Relativity led to treating the energy the object has when it is considered moving as a part of its mass when it is not.

#13

Whoo, okay here goes. The concept of ‘relativity’ in physics means that it is meaningless to talk about an object’s velocity in ‘absolute’ terms, only talk about velocity relative to another object. This was first elucidated by Galileo and is just as much a part of Newtonian physics as of Einsteinian physics. But when people talk about the ToR they usually mean one or both of Einstein’s theories. This is 'cos Einstein took the relativity ball and ran with it (relative to the Earth), so to speak.

In the mid-late 19th c, Maxwell worked out the laws of electromagnetism, including the discovery that light was a form of electromagnetic wave. This posed problems for the “Galilean” version of relativity as it was understood at the time. Firstly, you derive the speed of e-m radiation from Maxwell’s equations, without at any time talking about a frame of reference (i.e. what the speed is relative to). This implies that the speed of light (in a vacuum btw) is a constant regardless of the motion of the observer, which seems nonsensical. If a car is trundling along at 60mph down a motorway, and another car is going 50mph in the other direction, we would say the first is going at 60mph relative to the earth, 110mph relative to the second car, or 0mph relative to the driver of the first car. It seems impossible that there could be another object which all three observers simultaneously measure going at, say, 70mph. But light seems to do just this (except at 300,000kps).

[this next bit I’m shaky on]Another problem, which is the one that Einstein used to introduce his theory of Special Relativity, is what happens when a moving magnet induces an electrical current in another wire. This should occur regardless of whether the magnet or the wire is ‘really moving’, but Einstein showed that, as the principle of relativity was understood at the time, one situation would produce a current and the other would not. Experimentally, it made no difference, as we would expect.

Einstein solved this problem in his 1905 paper. He takes two postulates as unshakeable. Firstly, the principle of relativity. Secondly, the constancy of the speed of light (i.e. its independence of the motion of the observer). By insisting these two apparently contradictory notions must both always hold, he showed the real problem was in the way we were changing co-ordinates in switching between observers. Basically we had the wrong ideas about space and time. Einstein showed how to transform them correctly. (The math form of the transformations had been found earlier by Lorentz, but for him they were only an ‘interesting fudge’, Einstein showed the physical basis for them)

The consequences of this constitute Einstein’s “Special Theory of Relativity” of 1905. Standard results include things like

  1. moving objects are ‘squashed’ in the direction of their motion relative to the observer
  2. moving clocks run more slowly than their stationary counterparts
  3. two events that are simultaneous to one observer will not be to other observers (ie time does not flow at the same rate for everyone)
  4. relative velocities don’t add in the simple way we thought they did. With those two cars, the velocity of the first relative to the second is a teensy bit less than 110mph. For such low speeds the difference is negligible, but for speeds near that of light, the diff is important
  5. the momentum of a moving massive object is larger than just the ‘mv’ of Newtonian physics. This was originally thought of as saying that moving objects are heavier, but that point of view is deprecated these days.
  6. nothing with mass can travel faster than (or even at) the speed of light.
  7. E=mc^2, i.e. mass and energy are equivalent in a certain sense.

After his 1905 breakthrough, Einstein pondered the consequences to the existing theory of gravity. He came up with the ‘equivalence principle’ which basically says that for sufficiently small volumes of space, a gravitational field is equivalent to an accelerating frame of reference. This led in 1915 to his ‘General Theory of Relativity’, in which gravity is no longer thought of as a ‘force’, but rather is a twisting of space (or rather ‘spacetime’, as it had become more useful to think of space and time together as a four-dimensional entity at this point). This is much more complicated mathematically and it hurts my brane. Note it’s not just a ‘new way of looking at gravity’ but gives very different predictions when the grav fields are strong enough.

GR got experimental verification when it was predicted that grav fields bend light, and this was observed during an eclipse when the stars near it wobbled. Also it resolved a long-standing mystery about the precession of Mercury’s orbit, which I believe was about twice what Newton said it was supposed to be. It also predicts that grav fields mess time up. There was a cool experiment (Hafele-Keating?) where an atomic clock kept on a very fast aircraft for a while ran slow. And apparently it is crucial to take GR time corrections into account for GPS systems to work accurately.

You can also apply the equations of GR to the mass distribution of the universe as a whole, and so talk about cosmology. First time Einstein tried this, he got an expanding universe which appeared ridiculous. The equations permitted him to insert a ‘fudge factor’ called the cosmological constant, which would make the universe nice and static like it ‘obviously was’. Then Hubble realised the universe really WAS expanding so Einstein dropped the CC, calling it his ‘greatest blunder’. Weirdly, in the last ten years or so, cosmologists have discovered that the expansion of the universe appears to be accelerating. This appears to require bringing back the CC after all. Except in the age of Star Trek we call it ‘dark energy’.

A proper understanding of GR requires using mathematical objects called “tensors”. Nobody in the world knows what these are, and if they say they do, they are lying. :slight_smile: [/ego-protecting projection of my final-year physics degree difficulties]

#14

A James Maxwell reference ------ why you little demon you! :smiley:
Actually a very good post and my congrats to you.

#15

Einstein couldn’t explain relativity without using mathematics. When my grandfather asked him, he gave up in frustration.

So if he couldn’t, I probably couldn’t either.

#16

An object’s mass increases relative to its rest mass as its speed increases - divide its rest mass by the square root of {one minus {its velocity squared / velocity of light squared} }. Since this yields infinite mass at light speed, no object unless massless can be accelerated to lightspeed; however, differences in mass are minuscule until speed approaches a respectable fraction of lightspeed. The differences are still large enough to account for anomalies in the precession of Mercury’s perihelion, formerly attributed to the gravity of an unobserved Sun-grazing planet.

Light cannot travel faster than light - if a moving object emits light, this light has exactly the same speed in every direction. Instead, light emitted by a moving object has higher energy (shorter wavelength, higher frequency) in the direction of movement (“blue shift”), lower energy in the opposite direction (“red shift”). These effects are comfortably large enough for us to measure the rate at which distant galaxies are receding from us, and hence to predict a correlation between red-shift and absolute distance.

Time passes more slowly for a fast-moving object. The dilation factor is similar to the mass factor quoted above. This can be experimentally verified with a bodaciously accurate clock carried on a fast aeroplane or by noting that fast subatomic particles decay more slowly than slower editions of the same.

Matter and energy are equivalent - mass can be annihilated in certain subatomic interactions, resulting in the creation of a corresponding amount of energy. The conversion factor is the square of the speed of light in vacuo, that is, e = mc[sup]2[/sup]. That’s how atom bombs work and is also what fuels the Sun and other stars.

There is no single objectively correct frame of reference.

#17

Einstein developed the theory of relativity in the early 1900s. It upset Newtonian mechanics because it established that the speed of light © was a universal constant. Because the speed of light is the same in all frames of reference, regardless of whether they are moving, it means that we have to deal with four-dimensional space: events can take place at the same point in the space-time continuum but that simultaneity in 3-dimensional space is relative to how fast you’re moving.

For instance: if I shoot a beam of light out of a moving train, in a purely Newtonian universe my friend standing outside the train would say it moves at c + speed of train, and I would see it moving at c. However, this is not the case, because my friend and I both see it moving at c. My friend has to conclude that I shot the beam of light at time A, but I think I shot it at time B - OR that I shot it from point B, but my friend thinks I shot it at point A. We can’t agree on both the time and the place at which I shot the beam, only one of those two.

What this means is that the relative velocity of an object from one frame of reference to the other has a factor somewhere of (c+v) /c, where v is the velocity of the moving frame. For most things that we observe (such as a moving car), the object is moving at a speed so much slower than light that (c+v) / c ≈ 1. But this really does matter when the object is moving at a speed close to c, and that’s why if I run along the top of a train moving at, say, .75C, I still can’t exceed c.

#18

Posting without reading any other replies first, since OP wants what I know.

I just saw something on tv about this, so my recollection is sharper than might otherwise be the case. If I am driving in a car at 50 miles an hour, and am passed by a car going 60 miles an hour, I will perceive his speed to be 10 miles greater than my own. If I were stationary and passed at 60 miles per hour I would perceive his speed to be 60. So in other words, when we are both in motion, I perceive only the difference between our speeds, not their actual total velocity.

#19

In brief:

Depending on your point of view, the same action can have different observed characteristics–for example, a guy on a train measures the ground going by at 50mph but the train itself as stationary relative to himself, and vice-versa for a guy on a platform watching the train go by. This is the essence of the concept of a reference frame. Oh yeah, and there’s no such thing as the basic or true reference frame, and we wouldn’t be able to tell the difference even if there was.

The idea that the speed of light is constant for all observers regardless of their reference frame means that weird shit happens to one’s perception of time and spatial dimensions as one’s reference frame accelerates nearer to the speed of light.

#20

Okay, I’ll take a shot.

I know it’s e=mc2 (my brain doesn’t know how to do exponential numbers). Energy and mass can be converted into each other with a small amount of mass becoming a large amount of energy. Which is the basis for nuclear wepaons.

Einstein developed the Theory of Relativity. I know there are actually two kinds: General Relativity and Special Relativity but I’m not sure what the distinction is between them. I think General Relativity affects most of the objects in the universe while Special Relativity affects objects moving at near light speed.

I know that relativity says that space and time are connected and that your motion through space will affect how you preceive your motion through time. I believe that mass causes a distortion in time and space and this is what we perceive as gravity.