What is the theory of relativity?

Factual Questions
21

There’s two separate questions that people are answering here. First, is where do these two theories come from. The simpler theory, special relativity, comes from two assumptions: First, the assumption that the laws of physics look the same regardless of how fast you’re moving. In other words, you can’t say absolutely whether something is moving or stopped. There’s nothing new to this; Galileo had a good handle on the situation here. The second assumption, as proved by the M-M experiment and various theoretical considerations (Al didn’t actually know about the M-M experiment until after he published), is that the speed of light is the same as measured by all observers. If you put these two assumptions together and crank through the math (which isn’t actually all that complicated; the most advanced it gets is the Pythagorean Theorem), then you’ll get Special Relativity. For General Relativity, you need the two assumptions of SR, plus the assumption that gravity and acceleration are indistinguishable. In order to make this work, you need some rather …interesting… geometry, so GR isn’t as easy as SR.

The more interesting question, which doesn’t seem to have been addressed well yet, is what these theories mean. In simplest terms, SR states that space and time are related in almost the same way that the different spatial dimensions are related. For instance, you might have a cardboard box that’s 4’ wide, 3’ high, and 12’ long. None of those are absolute, though. If you turn the box around and stand it up, then you now have a box that’s 3’ wide, 12’ high, and 4’ long. On the other hand, if you measure the long diagonal of the box, it’ll always be 13’, no matter how you rotate it. Similarly, the length between two events and the duration between them can change when you “rotate” your reference frame through spacetime, by travelling at a different speed, but there’s something called the spacetime interval (equivalent to the long diagonal of the box) which stays the same no matter what your speed.

Explaining GR is a bit more complicated. Newton said that if there’s no forces acting on an object, then the object will go from point A to point B along the shortest path through space. In GR, what Einstein basically said was that gravity isn’t a force, and that objects travel from point A to point B along the “shortest” path through spacetime. In other words, if you want to get from right here, right now, to the opposite side of the Sun, six months from now, the shortest path through spacetime would be along the Earth’s orbit.

A few other minor points: First, how fast something has to be moving before SR becomes relevant depends on how you define “relevant”. At speeds of .1 c, the answers given by relativity and Newtonian mechanics will differ by about a percent. However, the relativistic effects are always there, and potentially measureable at speeds of a few millimeters a second. Second, physicists nowadays don’t usually talk about the mass of a particle changing; there’s other, cleaner ways to get the desired results out of the equations. Third, when you’re in orbit, you’ve got gravity involved, so you need to use GR. Since GR includes all of the assumptions of SR, the answer you get will already take all of the SR effects into account.

22

Thanks Chronos - your moniker certainly seems fitting.

I don’t want to trouble you, but I am wondering if you could expand on your analogy of a spacetime interval with an example, much like the box example for length, width and height. I have been trying to do so, but either am getting stuck or am having difficulty fully mapping the analogy.

Two events are separated, like the opposite corners of a box, by…hmmm, time, distance and speed the events are moving relative to one another? Or is it time relative to one another, distance, and finally speed relative to one another? And what does the spacetime interval measuring that is analogous to the diagonal length of the opposite corners of the box? The spacetime interval represents the absolute (because if it remains the same regardless of frame of reference, it’s absolute, right?)- what? Distance between the events across both space AND time?

Thanks for helping us dilettante non-professionals, here…

23

Thanks Chronos - your moniker certainly seems fitting.

I don’t want to trouble you, but I am wondering if you could expand on your analogy of a spacetime interval with an example, much like the box example for length, width and height. I have been trying to do so, but either am getting stuck or am having difficulty fully mapping the analogy.

Two events are separated, like the opposite corners of a box, by…hmmm, time, distance and speed the events are moving relative to one another? Or is it time relative to one another, distance, and finally speed relative to one another? And what does the spacetime interval measuring that is analogous to the diagonal length of the opposite corners of the box? The spacetime interval represents the absolute (because if it remains the same regardless of frame of reference, it’s absolute, right?)- what? Distance between the events across both space AND time?

Thanks for helping us dilettante non-professionals, here…

24

[hijack]

One thing I forgot to mention - DPWhite said that Einstein’s book “Relativity” is a great reference tool. I actually have the first U.S. edition of that book from 1920 (printed at the same time as the UK edition, both are considered the first English-language translation of the Special and General theories that were generally available.)- with a dust jacket even! :smiley: (we book collecting types dig having the dj, especially for books from before 1930). Definitely a rare book…

As a book collector, this is definitely one of my favorite books in my collection. I have pored over it several times, and while it is informative, it is heavy on math and light on analogies, both of which limit me.

[/hijack]

25

Well, events do not move. An event is a point in space at a moment in time. The corners of a box are not events. The opposite corners of a box at a particular time are events.The formula distance is Euclidean space is

ds [sup]2[/sup] = dx[sup]2[/sup] + dy[sup]2[/sup] + dx[sup]2[/sup]

Where ds is the distance between two points, say A and B, dx, dy and dx are the distances measured along the X, Y, and X axes. If you rotate the box (or your axes), dx, dy, and dx, may change, but ds[sup]2[/sup] is invariant. Note that if distance between A and B is zero, then A = B.

In Special Relativity, the equivalent formula is:

ds[sup]2[/sup] = (c *dt) [sup]2[/sup] - dx[sup]2[/sup] - dy[sup]2[/sup] - dx[sup]2[/sup]

Of course, if you use God’s units, c is one and can be eliminated from the equation. dt is the time interval in your reference frame. Note the minus signs. If ds[sup]2[/sup] is positive, the interval is time-like and you can find a frame where the two events occur at the same place and the time is at a minimum. If the separation is time-like, the time order is always the same. If ds[sup]2[/sup] is negative, the interval is space-like. If the separation between event A and B is space-like, in some reference frames, Event A occurs before event B and in others event B is before A. And in some frames, A and B are simultaneous. That is, simultaneity is relative. ds[sup]2[/sup] is zero on null-intervals. Points along a path of light are separated by a null-interval. This measure has the peculiar property that the interval between two events can be zero for events that are not equal.

26

DrMatrix (by the way, what happened to your hadron?)

a few questions:

  1. What are “God’s Units”? I suspect there may be humor in there, but since I am earnestly reading this trying to learn I am apt to let the humor-stuff get right past me…

  2. I get the impression that dx, dy and dz (I assume you meant dz and not a second dx) remain distance (or, to use your parlance, space-like) measures - similar to Chronos’ box analogy - in other words, if the cdt component didn’t exist, we’d in fact be talking about the box analogy all over again. The cdt component is the time component - therefore if the time part is bigger, it’s time-like; the time part is smaller, it’s space-like - right? well then:

    • What if they are equivalent and cancel each other out? Is that impossible, or a singularity or something?
      (ooops, I am re-reading where you say that ds2= 0 when there is a null interval - okay, then, what is that?)
    • If space-time is a contiguous variable, why does it appear that there is a clear delineation between the two types? Can something hover between space-like and time-like? With e=mc2 I always got the impression that matter and energy are equivalent, but not necessarily the same things - awkward phrasing, but I mean that one has the potential to be turned into the other, but it is not a smooth transition. Since physicists refer to a “space-time continuum”, I assumed that in relativistic terms, the transition between the two, is anything, isn’t required because they are woven into the same fabric - how big are my misconceptions?

Sorry for asking for a full physics lesson…

27

…if time and space are relative…

why don’t I get any birthday or christmas presents from them? :smiley:

28

  1. God’s units are the units where c equals one. If time is measured in seconds and distance in light-seconds, c is one. Which is as God intended.

  2. Wow! Long question. Let’s see. . . If I have two (distinct) events A and B. The interval between them does not depend upon the observer. The interval can be space-like, time-like, or null - corresponding to ds[sup]2[/sup] being negative, positive or zero. If two events are separated by a null interval, a light beam can travel from one to the other. Say Event A is at the origin, at time t=0, event B is on the x axis where x=1 (light-sec) at t=1 (sec). The interval is null. Different frames may assign different coordinates to the two events A and B, but if the separation is null (or space-like or time-like) in one frame, the separation is null (or space-like or time-like respectively) in all frames.

It is easier to visualize if you eliminate one spatial dimension, like z, and replace it with a time-axis. If the origin emits a pulse of light at time t=0, the light will trace out a cone, called a light-cone. The interior of the cone is the events separated from the origin by a time-like interval. The events on the cone are separated from the origin by a null-interval and the events outside the light-cone are separated from the origin by a space-like interval. If you reflect the light cone through the t=0 plane, you seperate space into three regions (four counting the cones themselves). The events inside the upper light-cone are called the origin’s absolute future. These are all the events that the origin can possibly affect. The events inside the lower light cone are the events in the origin’s absolute past. These are the events that could possibly have an effect on the origin. The events outside of the two cones are the absolute elsewhere. There is not enough time for a signal to get from the origin to elsewhere or from elsewhere to the origin. These events have no cause-effect relationship with the origin event.

Time is a dimension, but it is different from the other three dimensions. It is the (4D) space of all events that is a continuum.

If we use God’s units in E = mc[sup]2[/sup], we get E = m. Which says energy is mass or that mass and energy are two forms of the same thing - mass-energy. Before General Relativity, The conservation of mass and the conservation of energy were two distinct laws. E = mc[sup]2[/sup] says that mass can be converted to energy and the two conservation laws are combined into the conservation of mass-energy.

Virtually yours,

DrMatrix — Quit staring at my hadron!

29

Many physicists prefer to define ds[sup]2[/sup] = dx[sup]2[/sup] + dy[sup]2[/sup] + dz[sup]2[/sup] - c[sup]2[/sup]dt[sup]2[/sup] (signs opposite of the way that DrMatrix listed it, but the math works either way, as long as you’re consistent. Personally, I prefer to make the time component positive and the space components negative, (as the good doctor did above), but we’re in the minority.

I’ll also add that God’s units are also usually taken to mean that hbar (Planck’s constant over 2pi), G, Boltzman’s constant, and Coulomb’s constant are also one, depending on context (for instance, a particle physicist usually doesn’t bother with G, and a gravitational physicist usually doesn’t bother with hbar). If you use the full set of God’s units, as in an attempted Unified Theory, you end up being able to express everything as a pure number, without any units attached to anything. The idea is that those constants are so fundamental, that God created the Universe in terms of those constants, so His units are the ones based on those constants. I’m not sure if it should be considered humor or not, but physicists really do talk in such terms.

30

Cool - thanks for the explanations, especially with the light-cone visual (I told you I was better with analogy - that extends to visuals, too…)

One last point of clarification: I apologize, but the whole “null interval” things still has me flummoxed. The time-like and space-like I am doing well with, especially with the light cone explanation: time-like means that the event at time zero is affected by or can affect events separated from it by a time-like interval. Space-like sounds like there can be no causal relationship because there is a space interval (i.e., distance) between the two events. Where does a null fit in? Your explantion in the previous post:

“If two events are separated by a null interval, a light beam can travel from one to the other. Say Event A is at the origin, at time t=0, event B is on the x axis where x=1 (light-sec) at t=1 (sec). The interval is null.”

Doesn’t clarify it enough for me. Are there examples, explanations full of one-syllable words, something for this layman to better grasp?

Thanks for your patience,

Word(obviously not Physics)Man

31

A null interval is also called a lightlike interval for just this reason (because it’s more confusing than the other two), WordMan. I suppose you could think of events with lightlike separation as something where you can send a signal from the one to the other, but there’s not enough time for the signal to actually DO anything.

So an example of two events with null separation would be me shooting a laser at you and you first getting hit by the beam. The signal has arrived, but it’ll take some tiny amount of time for the laser beam to actually DO anything to you.
[hijack, for more experienced physicsy people]
I’ve noticed that of the older people I know in phyiscs, the relativists tend to use a positive metric and the particle physicists and field theorists tend to use a negative trace metric. Is this just a wacky coincidence, and if not, why on earth did things develop like this?
[/hijack]

32

Interval in SR is similar to distance in Euclidian geometry, but they are not quite the same. Null-intervals illustrates one of the differences. The distance between a point and itself is zero, as is the interval between an event and itself. But the interval between distinct events can be null. Every event has a light cone (defined above). The interval between two events is null exactly when they lie on each other’s light cones.

[** g8rguy**'s hijack continued]
Which are you calling the positive metric and which the negative? I feel comfortable with both forms. As Chronos pointed out, they are equivalent. I started out with time-like intervals being positive and Chronos says he prefers that form. So, in this thread, time-like interval are positive so as not to confuse the non-experienced physicsy people any more than they already are.
[/hijack]

33

[with apologies to the rest of the world, my hijack continued yet further]
I’m calling the positive metric the one with positive trace: -+++. I don’t mind using either -+++ or ±–, and of course it doesn’t matter anyway, although I’m glad to see we’re using ±-- here, since I prefer it. What I DO mind is that after almost a century, we still haven’t established a convention, and it means that when, for example, I read one paper that uses ±-- and another that uses -+++, I have to be extra careful to keep which choice the authors made fixed in mind. But I’ve noticed that most relativists I know use -+++ and most field theorists I know use ±–. I was wondering if this is just happenstance, or if this is a pseudo-convention.
[/hijack, and hopefully my last word on this]