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physicist2

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General theory of relativity …

Special theory of relativity ...

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In summary: So don't expect a lot of technical detail. Just give a high level overview of the two theories and what they cover.In summary, General theory of relativity focuses on the effects of gravity on motion, while special relativity covers the effects of motion on gravity.

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physicist2

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General theory of relativity …

Special theory of relativity ...

Thank you.

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- #2

jedishrfu

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Are your questions related to a homework assignment?

Wikipedia is a useful reference for these kinds of questions with links to other more descriptive sources.

Here's another reference:

http://www.geekpolice.net/t8544-what-is-relativity-simple-explanation

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Cosmobrain

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SR is based on two principles.

If you travel at near the speed of light, another observer "standing still" will notice three effects on you:

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

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PeterDonis

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Cosmobrain said:GR is pretty much the same thing. However, it includes acceleration and gravity.

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

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PeterDonis

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Cosmobrain said:objects affected by it are actually inert.

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

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PeterDonis

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Cosmobrain said: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.

- #7

PeterDonis

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physicist2 said: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.

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atyy

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physicist2 said: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.

physicist2 said: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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Cosmobrain

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

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

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.PeterDonis said: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.

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

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PeterDonis

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jedishrfu said:

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:

https://www.physicsforums.com/showthread.php?t=511170

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.

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A.T.

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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:physicist2 said:in one or two sentences please.

https://www.youtube.com/watch?v=C2VMO7pcWhg

https://www.youtube.com/watch?v=DdC0QN6f3G4

- #12

PeterDonis

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Cosmobrain said: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.

Cosmobrain said: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.)

Cosmobrain said: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.

Cosmobrain said: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.

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Cosmobrain

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PeterDonis said: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

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PeterDonis

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Cosmobrain said: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.

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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.

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danjordan

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Al's Relativistic Adventures: http://www.onestick.com/relativity/

World Science U (with Brian Greene): http://www.worldscienceu.com/

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Happy Recluse

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Cosmobrain said: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"?

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Happy Recluse said: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.

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Matterwave

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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.

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Happy Recluse

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pervect 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.

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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.

Happy Recluse said: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.

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Happy Recluse

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pervect said:"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.

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Nugatory

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Happy Recluse said: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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Happy Recluse

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Nugatory said: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##?

- #25

Nugatory

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Happy Recluse said: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.

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Happy Recluse

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It is true that Smith claims the pattern of the bouncing ball is straight. It is true that Jones claims the pattern of the bouncing ball is not straight. Here we agree. Is it true that the pattern is both straight and not straight?

Here's an example. Smith and Jones observe a criminal suspect. Smith says the suspect is male; Jones says the suspect is not male. No one reports that the suspect is (in fact) male and not male.

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Matterwave

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- #28

Nugatory

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Happy Recluse said:It is true that Smith claims the pattern of the bouncing ball is straight. It is true that Jones claims the pattern of the bouncing ball is not straight. Here we agree. Is it true that the pattern is both straight and not straight?

When Smith says "the pattern of the bouncing ball is straight up and down", I understand that statement as Smith meaning "the ball is moving on a path that takes it up and down but not left and right or forwards and backwards

When Jones says "the pattern of the bouncing ball is straight up and down", I understand that statement as Jones saying "the ball is moving on a path that takes it up and down but not left and right or forwards and backwards

It's possible, because of that all-important phrase "relative to me" for the ball to be bouncing up and down according to Smith but not Jones, or vice versa, without requiring that one of them be wrong.

Here's an example. Smith and Jones observe a criminal suspect. Smith says the suspect is male; Jones says the suspect is not male. No one reports that the suspect is (in fact) male and not male.

Suppose that Smith reported that "the suspect and I are the same gender" and Jones reported that "the suspect and I are not the same gender". Now we have (Thomas) Smith saying P and (Audrey) Jones saying not-P, yet they are both right and there is no contradiction.

The "straight up-and-down bounce" report works the same way; the notion of up and down is defined relative to an observer so different observers can make different statements about whether the motion is up-and-down without contradiction.

Perhaps the most important thing for understanding physics is learning the difference between frame-dependent quantities ("Is the bouncing ball moving straight up and down?", "Is the suspect of the same gender as you?") and frame independent quantities ("What is the world-line of the bouncing ball?", "What is the gender of the suspect?").

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Happy Recluse

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Matterwave said:

Thank you. With your analogy, we know that both judgments can be true: the suspect has a face and a back to his head. But suppose Smith says, "The face has a mole between his eyes," and Jones says, "The [same] face has no moles on it." Here, both

Again, using your analogy, and back to the bouncing ball, Smith says, "The ball has a red stripe on it," and Jones says, "The ball has a blue star on it." Both judgments can be true. But if Smith says, "The ball bounces in a straight line," while Jones says, "The ball does not bounce in a straight line (because it bounces in a W pattern)," both judgments cannot be true.

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Happy Recluse said:Thank you. With your analogy, we know that both judgments can be true: the suspect has a face and a back to his head. But suppose Smith says, "The face has a mole between his eyes," and Jones says, "The [same] face has no moles on it." Here, bothcannotbe true. (There might be confusion about what a mole is, but we still know that both cannot be true no matter our understanding of moles. That is Smith says, "The face has X on it," and Jones says "The face has no X on it.")

Sure, both cannot be true because this is a frame-independent statement.

Again, using your analogy, and back to the bouncing ball, Smith says, "The ball has a red stripe on it," and Jones says, "The ball has a blue star on it." Both judgments can be true. But if Smith says, "The ball bounces in a straight line," while Jones says, "The ball does not bounce in a straight line (because it bounces in a W pattern)," both judgments cannot be true.

Here we have a frame-dependent statement. This is why both statements can be simultaneously correct. This also means that "bouncing in a straight line" is not an absolute statement, but a relative one.

The general theory of relativity is a theory of gravitation developed by Albert Einstein in 1915. It describes the effects of gravity as a curvature of space and time caused by the presence of mass and energy.

The special theory of relativity is a theory developed by Albert Einstein in 1905, which describes the relationship between space and time in the absence of gravity. It states that the laws of physics are the same for all observers in uniform motion.

The main difference between the general and special theory of relativity is that the general theory includes the effects of gravity, while the special theory does not. The general theory also provides a more comprehensive and accurate description of the universe.

The general theory of relativity explains gravity as a curvature of space and time caused by the presence of mass and energy. Objects with mass cause a distortion in the fabric of space-time, which is perceived as gravity.

The theory of relativity has numerous practical applications, including GPS systems, which use the theory to account for the effects of time dilation caused by the satellites' high speeds. It also helps in understanding the behavior of black holes and the expansion of the universe.

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