General and special theory of relativity in few words

How can I explain to someone who has only high school level of education in physics, what is general and special theory of relativity about? Each of them separetelly in one or two sentences please.

General theory of relativity …

Special theory of relativity ...

Thank you.

It is not that easy. However I can try to synthesize it. Starting by the special theory of relativity:

SR is based on two principles. 1-The speed of light in a vacuum is always constant, no matter the speed of the observer who is measuring it. 2- In any frame of reference, the laws of physics must be the same.
If you travel at near the speed of light, another observer "standing still" will notice three effects on you: Time dilation (your clock will seem to be slower), length contraction (you will get shorter in the direction of your motion) and increased mass (E=mc², the energy of motion turns into mass rather than velocity)

GR is pretty much the same thing. However, it includes acceleration and gravity. Gravity is described as a curvature in space-time, and objects affected by it are actually inert. When you're in a strong gravitational field, time will seem to run slower for you in the point of view of an observer outside.

cb

PeterDonis
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GR is pretty much the same thing. However, it includes acceleration and gravity.

This isn't quite correct; SR can handle acceleration.

PeterDonis
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objects affected by it are actually inert.

What do you mean by this? I'm not sure what you're referring to.

PeterDonis
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When you're in a strong gravitational field, time will seem to run slower for you in the point of view of an observer outside.

One clarification here: this is only true for certain situations, where the gravitational field is produced by an isolated body that is basically static (like a planet or star or black hole). It is not true in the more general case (such as for the universe as a whole), because there is no meaningful way to define "an observer outside" to serve as the standard against which "time running slower" is measured.

PeterDonis
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How can I explain to someone who has only high school level of education in physics, what is general and special theory of relativity about?

Cosmobrain's answer is a pretty good quick summary (other than the things I've addressed in separate posts). I would just add a couple of quick points:

* Motion is relative; for example, I am not moving relative to the Earth at this moment, but I am moving relative to the Sun.

* Physics can be expressed entirely in terms of invariants, i.e., quantities that are the same regardless of which frame of reference you choose.

atyy
Special theory of relativity ...

A theory about the symmetry of the laws of physics without gravity. The laws of physics without gravity have a symmetry such that the speed of light is the same for any measurement system moving at constant velocity. Here spacetime is flat.

General theory of relativity …

A theory of gravity in which gravity is the curvature of spacetime. Matter tells spacetime how to curve, and spacetime tells matter how to move. In regions of spacetime small enough to be considered approximately flat, special relativity is a good approximation.

I made a tiny lie above: one can also get gravity in special relativity by describing gravity as a massless spin 2 field, but I don't think this method gives the full range of gravitational phenomena in general relativity such as the accelerating expanding space of cosmology.

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Oh well, here we go again.

This isn't quite correct; SR can handle acceleration.
Fine. Ok then, then it just can't handle gravity

What do you mean by this? I'm not sure what you're referring to.
I'm saying an object is traveling in a straight line as it normally would, however, space itself is distorted, so it curves and it seems like the object was affected by a force.

One clarification here: this is only true for certain situations, where the gravitational field is produced by an isolated body that is basically static (like a planet or star or black hole). It is not true in the more general case (such as for the universe as a whole), because there is no meaningful way to define "an observer outside" to serve as the standard against which "time running slower" is measured.
I had in mind that the object A was, say, on Earth and the and observer B was in space watching A. Object A can be the surface of the planet and B can be a GPS satellite. GPS satellites work with SR and GR.

Remember we are explaining relativity in a synthesized way to a high schooler.

PeterDonis
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This isn't a bad summary, but it does make one common misstatement that is known to cause confusion in people learning the theory for the first time:

Einstein said that all observers will measure the speed of light to be 186,000 miles per second, no matter how fast and what direction they are moving.

This maxim prompted the comedian Stephen Wright to ask: "If you are in a spaceship that is traveling at the speed of light, and you turn on the headlights, does anything happen?"

The answer is the headlights turn on normally, but only from the perspective of someone inside the spaceship. For someone standing outside watching the ship fly by, the headlights do not appear to turn on: light comes out but it takes an eternity for the beams to get ahead of the spaceship.

What should have been said here is that the spaceship can't travel at the speed of light, and the idea of "the perspective of someone" who is traveling at the speed of light is meaningless. We have a FAQ on this:

For a spaceship traveling at *almost* the speed of light, someone watching it fly by will indeed see the headlights turn on, and the light from them will travel at the speed of light. The person watching will see the light pull ahead of the ship slowly (because the ship is traveling at almost the speed of light), but that doesn't prevent the headlights from appearing to turn on.

A.T.
in one or two sentences please.
Take the fist one or two sentences from Wikipedia. Of course that's not enough to understand anything, but you cannot do more with one or two sentences. Alternatively you can use these short visual introductions:

PeterDonis
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Ok then, then it just can't handle gravity

Yes. I pointed out that SR can indeed handle acceleration because thinking that it can't is not only a common misconception, but ignores a *huge* body of experimental evidence for SR, namely, all the experiments we do in particle physics, which involve subatomic particles being subjected to huge accelerations and behaving exactly as SR predicts.

I'm saying an object is traveling in a straight line as it normally would, however, space itself is distorted, so it curves and it seems like the object was affected by a force.

Ok, that makes it clearer. But it still might confuse someone encountering it for the first time, because you say the object travels in a straight line and then you say it curves. I would say "the object's trajectory appears to curve and it seems like the object was affected by a force".

(I would also say *spacetime* is distorted, not space; for most cases of practical interest, such as planets orbiting the Sun or satellites orbiting Earth, the effect of space curvature is negligible; the curvature that affects the trajectory is curvature in the time dimension.)

I had in mind that the object A was, say, on Earth and the and observer B was in space watching A.

Yes, I understood what you had in mind. I was just pointing out that GR covers a wide range of situations, of which this is only one, so that it's clear that "gravitational time dilation" is a feature of this particular situation, not of GR in general.

Object A can be the surface of the planet and B can be a GPS satellite. GPS satellites work with SR and GR.

Remember we are explaining relativity in a synthesized way to a high schooler.

Then GPS is probably not a good example to use, precisely because it requires combining SR and GR (i.e., it requires understanding and combining both the effects of relative motion *and* the effects of gravitational time dilation) to correctly interpret what is going on.

Yes. I pointed out that SR can indeed handle acceleration because thinking that it can't is not only a common misconception, but ignores a *huge* body of experimental evidence for SR, namely, all the experiments we do in particle physics, which involve subatomic particles being subjected to huge accelerations and behaving exactly as SR predicts.

Ok, that makes it clearer. But it still might confuse someone encountering it for the first time, because you say the object travels in a straight line and then you say it curves. I would say "the object's trajectory appears to curve and it seems like the object was affected by a force".

(I would also say *spacetime* is distorted, not space; for most cases of practical interest, such as planets orbiting the Sun or satellites orbiting Earth, the effect of space curvature is negligible; the curvature that affects the trajectory is curvature in the time dimension.)

Yes, I understood what you had in mind. I was just pointing out that GR covers a wide range of situations, of which this is only one, so that it's clear that "gravitational time dilation" is a feature of this particular situation, not of GR in general.

Then GPS is probably not a good example to use, precisely because it requires combining SR and GR (i.e., it requires understanding and combining both the effects of relative motion *and* the effects of gravitational time dilation) to correctly interpret what is going on.

Well, write your own definition of SR and GR. It would be better ;)

cb

PeterDonis
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Well, write your own definition of SR and GR. It would be better ;)

If I were to rephrase yours, it would be basically what atyy wrote.

pervect
Staff Emeritus
I'll offer a rather unconventional approach, and an explanation of why I'm sugesting it. Here are the defintions I'd propose:

Special relativity gives you the ability to draw, manipulate, and transform maps of space-time, called space-time diagrams, in regions without gravity.

General relativity gives you the same abilities (to draw, manipulate, and transform maps of space-time) in regions with gravity.

It perhaps over-emphasises the importance of space-time diagrams to the theory, but the goal is to lead the listner into further studying the not-terribly complex idea of space-time diagrams, so that they can progress on to more advanced explanations.

In any frame of reference, the laws of physics must be the same.
cb

It seems that this premise gets translated into "if two observers report different things, both of the reports are true." For example, the observer bouncing a ball on a moving railroad car reports the ball moving straight up-and-down, while the stationary observer watching the ball reports it moving in a W pattern. So, how do we go from "the laws of physics are the same" to "both reports are true"?

pervect
Staff Emeritus
It seems that this premise gets translated into "if two observers report different things, both of the reports are true." For example, the observer bouncing a ball on a moving railroad car reports the ball moving straight up-and-down, while the stationary observer watching the ball reports it moving in a W pattern. So, how do we go from "the laws of physics are the same" to "both reports are true"?

First you need to describe the motion of the ball in one frame. This is done via the branch of physics known as kinematics. which is "the study of classical mechanics which describes the motion of bodies without consideration of the causes of motion", i.e.forces. (this definition is from wiki, though it was simplified a bit for clarity of presentation).

Kinematics also tells you how to transform the motion of the ball in one frame to another frame as well as describe the motion of the ball in one frame. Pre-relativity, the laws of kinematics use the Galilean transform to transform the motion, post-relativity, the laws of kinematics use the Lorentz transform.

http://en.wikipedia.org/wiki/Galilean_transformation
http://en.wikipedia.org/wiki/Lorentz_transformation

I would describe the "laws of physics" which are the same in both frames as the "laws of dynamics". This involves solving for the motion of the ball, given its dynamical characteristics, in a mannner which DOES consider the "causes of motion", (traditionally in high school the cause of motion is considered to be forces, but if you have advanced training in physics you may use the Lagrangian or Hamiltonian formulation of physics to describe the causes of motion).

The point of this is that if you solve for the motion of the ball using the laws of dynamics in the train frame and then use the laws of kinematics to transform the solution to the stationary frame, you must get the same solution that you get using the laws of dynamics directly in the stationary frame.

Similarly, if you solve for the motion of the ball using the laws of dynamics in the stationary frame and then use the laws of kinematics to transform the solution to the train frame, you must get the same solution that you get using the laws of dynamics directly in the train frame.

Matterwave
Gold Member
I would probably say:

Special relativity is the theory, published in 1905 by Einstein, which modified Newton's worldview on the motion of objects. It gives rise to many fascinating phenomena, which can be felt only when things are moving very fast, including time dilation and length contraction.

General relativity is the theory, published in 1915 by Einstein, which included gravity into the previous worldview given by special relativity. In the presence of strong gravitational fields, GR gives rise to effects such as the gravitational time dilation, the bending of light rays, as well as the gravitational redshift. It is the framework on which all of our understanding of the large scale structure of the universe is based.

Similarly, if you solve for the motion of the ball using the laws of dynamics in the stationary frame and then use the laws of kinematics to transform the solution to the train frame, you must get the same solution that you get using the laws of dynamics directly in the train frame.

If your conclusion is that both reports are true, then the reports are inconsistent. One or both are false.

Are there branches of physics that explain illusions? Perhaps such a branch can explain that the stationary observer reports an illusion of the ball moving in a W pattern, while observing a ball, in a moving train, bouncing straight up-and-down.

pervect
Staff Emeritus
me said:
Similarly, if you solve for the motion of the ball using the laws of dynamics in the stationary frame and then use the laws of kinematics to transform the solution to the train frame, you must get the same solution that you get using the laws of dynamics directly in the train frame.

If your conclusion is that both reports are true, then the reports are inconsistent. One or both are false.

Are there branches of physics that explain illusions? Perhaps such a branch can explain that the stationary observer reports an illusion of the ball moving in a W pattern, while observing a ball, in a moving train, bouncing straight up-and-down.

"If both reports are true" is a bit ambiguous. If by this you mean that a stationary observer reports motion in a W pattern, while a moving observer reports straight up and down motion, this is not inconsistent either in special relativity or in classical Newtonian physics. I don't understand why you think there is a consistency problem, consistency is guaranteed by the existence of invertible transforms between the coordinate systems attacahed to frames of reference.

"If both reports are true" is a bit ambiguous. If by this you mean that a stationary observer reports motion in a W pattern, while a moving observer reports straight up and down motion, this is not inconsistent either in special relativity or in classical Newtonian physics. I don't understand why you think there is a consistency problem, consistency is guaranteed by the existence of invertible transforms between the coordinate systems attacahed to frames of reference.

The inconsistency lies between the two reports, i.e., the ball does not move straight up-and-down and not straight up-and-down (p and not-p). One of these two reports is true and the other is false. The inconsistency occurs even if no one knows which of the two is true.

Nugatory
Mentor
The inconsistency lies between the two reports, i.e., the ball does not move straight up-and-down and not straight up-and-down (p and not-p). One of these two reports is true and the other is false. The inconsistency occurs even if no one knows which of the two is true.

However, one observer uses the words "moving straight up and down" to mean that ##\frac{dx'}{dt'}=\frac{dy'}{dt'}=0## while the other uses these words to mean ##\frac{dx}{dt}=\frac{dy}{dt}=0##. Because these statements are not the same (the primed coordinates are not, in general, equal to the unprimed coordinates) this is not a "p and not-p" situation.

It's worth noting that this is a classical physics issue, around since long before Einstein - it's Galileo's work based on the Galilean transforms.

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However, one observer uses the words "moving straight up and down" to mean that ##\frac{dx'}{dt'}=\frac{dy'}{dt'}=0## while the other uses these words to mean ##\frac{dx}{dt}=\frac{dy}{dt}=0##. Because these statements are not the same (the primed coordinates are not, in general, equal to the unprimed coordinates) this is not a "p and not-p" situation.

It's worth noting that this is a classical physics issue, around since long before Einstein - it's Galileo's work based on the Galilean transforms.

Is the following true: ##\frac{dx'}{dt'}=\frac{dy'}{dt'}=0## is not ##\frac{dx}{dt}=\frac{dy}{dt}=0##?

Nugatory
Mentor
Is the following true: ##\frac{dx'}{dt'}=\frac{dy'}{dt'}=0## is not ##\frac{dx}{dt}=\frac{dy}{dt}=0##?

If you're asking whether it is possible for ##\frac{dx'}{dt'}## and ##\frac{dy'}{dt'}## to both be equal to zero when at least one of ##\frac{dx}{dt}## and ##\frac{dy}{dt}## are non-zero and they're describing the exact same motion of the exact same object in the primed and unprimed coordinates.... Then the answer is yes it is possible. Indeed, that will always be the case if the origin of one coordinate system is moving in the the x-y plane of the other.

And at the risk of repeating myself.... This is a completely classical result consistent with the Galilean transforms, no modern non-classical relativity theory involved.