What is the difference between the special theory of realtivity and the general theory of relativity?

Also, did I spell everything in the title right? It looks sort of funny.

This is really werid. This was discussed just today in my history of science class! This is how it was described to us: (I am not a physics majoy, I am just repeating what my professor said)

1.Special relativity: the laws of physics are the same for all observers in uniform motion.

2. General relativity:
Adds saying that it allows different frames of reference due to acceleration.

This is all with the assumtion of a constant veliocity of the speed of light.

So basically with the equation v=d/t than with a constant v, distance and time have to change/distort. So if everyone was moving at the speed of light, nobody will notice a difference. But if one person was moving slower, his perception of time or distance would change relative to the other person.



Yah i know its confusing. I barely understand it and i am very sure i got it wrong. But this is what i have down in my note (well I edited out some other stuff). If i am wrong can someone correct me please?

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It gets much more complicated on both a physics and mathematical level (I'm reading myself into it now).

Essentially, special relativity has two main postulates:
1) the speed of light is constant in all inertial reference frames
2) the laws of physics will remain the same no matter which reference frame they are applied.

General relativity has 3 main ideas:
1) spacetime is curved and can be described by mathematical "things" called pseudo-Riemannian manifolds
2) there are locally inertial reference frames (flat coordinates) in which the physics in GR are the same as in SR (known as the principle of equivalence - there is no experement that can distinguish an accelerating reference frame from a gravitational field)
3) mass curves spacetime (think of a bowling ball on a stretched out blanket; the ball makes a "dent" in the fabric, curving the are around it)

I think that's about it. Hope that helps

WhooHoo! i had the basics right. :-D

Everyone always like to go over relativity in terms of a train traveling at the speed of light. Without getting scientific at all, the basic difference is:

• Special relativity explains what happens when you are on a train traveling at the speed of light.
• General relativity explains what happens when a train traveling at the speed of light goes by you.

With my luck I've probably got that backa**wards, but if I remember the math and physics (which I hopefully remember more of than I do of trains), I think that makes sense.

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Matt Bisgaier
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Relativity explains why your train can't go the speed of light.

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Oops... make that very close to the speed of light. I knew there was a reason why I shouldn't be up early in the morning, much less up early in the morning trying to make sense. Coffee time!

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Matt Bisgaier
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Special relativity applies the experimental result that the speed of light is the same in all inertial frames to extend Newtonian physics to relativistic speeds.

General relativity explains why a person standing on a platform appears to accelerate backwards when you're in a departing train by introducing the idea of equivalence between gravity and acceleration.

The train analogy doesn't work for me. Wouldn't both the person on the train as well as the person standing at the station platform simply be 2 different inertial frames of reference, hence both fit snuggly into the realm of SR? I guess I always thought of GR simply as SR, but with accelleration taken into account (accel. being any "curve" in the path of an object). A simplistic view, granted, but I'm a simplistic kind of guy!

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No. The passenger on the platform observes you. He sees you accelerate relative to him with the train out of the station because of the ballet of forces with train. Everything fits. You are accelerating because there is a force applied to you.

Now, you observe the passenger on the platform. You seem him accelerate relative to you. But there is no force causing him to do that. Acceleration without force? Defies Newton's Second Law. You're in a non-inertial frame because the frame is accelerating with respect to an inertial one. That's where Newtonian mechanics fails. It applies only to inertial frames. It cannot be applied to non-inertial frames. An inertial frame is one where all accelerations observed are due to forces according to Newton's Second Law. An non-inertial frame is one that is accelerating relative to an inertial one.

The way to account for this is to presume a gravitational field acting in the opposite direction to your acceleration relative to the inertial. That explains why you feel like you're being pushed back into your seat and why the passenger on the platform appears to accelerate. It's this gravity equivalence.

General relativity found a way to consider the equivalence to be not only apparent, but actual.

I think if you're fixated on using a train analogy, you have to have the train accelerating for the general relativity. SR will work for either observer for a train moving at constant speed.

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Yes. The train is accelerating.

This may not be the difference you're looking for, but....

Special theory: easy.
General theory: hard.

The special theory is actually fairly easy to understand. And a high school student who's fair in math can handle the mathematics involved.

The general theory... well, the general idea isn't so tremendously strange. For the general theory Einstein adds the (very relevant) ideas of gravitation and acceleration into the mix, which were not treated in the special theory. And the math is considerably harder (but I guess something always seems harder when you don't have a good handle on it).

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glom:

That is part of Special Relativity, too.

ljbrs :wink:

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Which part? The equivalence of gravity and acceleration is not a part of special relativity.

Special relativity covers inertial frames only.

#-o I think I need a very, VERY big Tylenol and a practice nap.

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But even Einstein's original 1905 paper dealt with non-inertial effects (the "twin paradox"). Perhaps that is what she is referring to.

The twin paradox comes about because both see the other's clock as moving slow while the flight is in progress. The paradox is that on the return the space faring twin is younger. Since SR is limited to inertial (non-accelerated) referance frames, it cannot explain why there is an age difference. Hence the paradox.

In GR, which does include accelerated frames, there is no paradox. The space faring twin undergoes two major accelerations the ground-based one does not. The first is to launch the ship in the first place. The second is to turn the ship around at its destination and return it to earth. General relativity makes the correct predictions for the age difference of the twins and the reasons why are well understood and no longer paradoxical.

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"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

The twin paradox is strictly SR. It doesn't need to involve GR.

The fact is that in the twin paradox there are three inertial frames - the original, planet-bound frame, the frame in which the twin is moving away, and the frame in which the twin is moving back.

In order to get back to the planet, the twin needs to switch inertial frames, and that breaks the reciprocity. The acceleration, the means by which the twin changes frames, isn't really relevent, so neither is GR.

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SeanF

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There is still a paradox in the GR version, but not quite the one you're talking about. Which of the twins is younger at the moment the space-faring twin turns for home?

Let's assume that they are both at rest at the start relative to a third inertial frame. Then the space-faring twin makes his trip to his destination at a higher velocity than the stay-at-home, and so is younger when he turns for home.

But imagine that at the start both twins were flying through space away from the destination at a constant velocity relative to a fourth frame of reference. Now the space-faring twin has to slow down to get to the destination. So he's the older twin when he turns for home!

Identical situation, but the space-farer is the older twin in one frame, and the younger twin in another!

Of course, by the time he gets home, he'll be the younger twin in all frames (because the journey home requires that he accelerate to catch up with the stay-at-home).

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That's not right, Eroica - there's no difference between "speeding up" and "slowing down." They're both acceleration, and the GR effects would be the same.

The two twins would disagree on who's older at the time of turn-around, though - in fact, the space-faring twin immediately before the turn-around would disagree with the space-faring twin immediately after the turn-around!

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SeanF

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GR is relevant since that's the theory you need to use to handle accelerated reference frames (or gravitational fields). SR is "special" because it can only deal with the "special" case of intertial reference frames. The twin paradox arises because SR cannot explain why there would be an age difference upon return. Simply stated, the paradox asks why this should occur since each twin sees the other's clock as running slow. The answer is that the space twin undergoes accelerations at launch and turn-around that the earth twin does not. At this point SR breaks down since we no longer have two inertial frames. When the calculations are done with general relativity (which is "general" because it deals with all possible accelerations and gravitational fields) the correct answers are found and there is no paradox.

Think about all of the train and flashlight gedanken experiments that are use to illustrate SR. In all of them, the train has already reached a steady speed and does not accelerate or turn. That makes it an inertial frame. We don't worry about how it got there, just that it is.

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"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

You need GR to deal with accelerating reference frames, but you don't need to deal with accelerating frames in the twin paradox - they're there, but can be ignored. Consider this:

Put both the twins on spaceships sitting next to each other pointing in the same direction (they're in an inertial frame). Both ships begin accelerating uniformly and simultaneously, and reach .6c simultaneously, at which point they both cut acceleration and coast (in a new inertial frame). After a certain amount of time, one ship decelerates uniformly until it comes to a stop (relative to the starting point - back in the first inertial frame). The second ship continues to coast along for a while long, then goes through the same uniform deceleration and also stops.

The second ship (the one that went farther) then goes through a uniform acceleration back to .6c in the other direction. The first ship begins its uniform acceleration back in the return direction as the second ship approaches so that it reaches .6c as the second ship comes alongside. They they continue to coast back towards the starting point, where they simultaneously decelerate and stop at their original starting point.

Any and all GR / acceleration related effects can be discounted because they will be identical for both ships. However, the twin in the second ship will be younger. Why? Because of the SR effects of the different amounts of time spent in the different inertial frames.

In the standard twin paradox, of course, only one twin experiences acceleration (and the related GR effects), which will compound the age difference, but that twin is still younger as a result of simple SR effects - and the longer he coasts between accelerating and decelerating, the more difference in age there'll be.

There is no actual "paradox", even in SR, because the situation is not reciprocal. One twin remains in the same inertial frame through-out the experiment, while the other spends time in two additional inertial frames.

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SeanF

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No, you can deal with the problem in SR as well. As SeanF pointed out, there are three reference frames (the stationary twin, the inbound twin, and the outbound twin). If you formulate the problem to make the reference frames explicit then the paradox goes away. No need for GR.

I guess that's right, but there is a difference in the SR effects of travelling faster and travelling slower (after the accelerations are over). I still contend that I described the paradox correctly, but it's really an SR effect. At the turning point, one twin is older in one frame of reference and younger in another. :-k

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Actually, at any point while the twin is moving away from Earth, he's older in his own reference frame and younger in the Earth's reference frame.

After he's turned around and is heading back, he's younger in both reference frames, but there's disagreement as to how much younger - until he gets back to Earth and stops, at which point everybody agrees on everything!

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SeanF

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I'm in the midst of checking up on this one some more before making another declarative statement. But here's a preliminary observation. While one can resolve the twin paradox (calculate the age difference) using just the SR time dilation relations, you cannot explain why that time difference occurs without invoking the perception of the astronaut. Preferably, one (especially Einstein) wants to get a purely physical description that doesn't require an observer. One of the texts I'm looking at calls this "one of the loose ends that drove Einstein to go beyond the simple version of relativity (SR) we have studied so far."

The answer has to do with the effect gravitational fields (or accelerated frames, they are equivalent) have on clocks as a function of height. It's a well known (and experimentally proven) consequence of GR that clocks at high altitude run faster than those at ground level. The effect is proportional to the acceleration and the height. For the spaceship changing direction at the distant star both the "height" (in this case the distance to earth) and the acceleration are large. The overall impact is that during the turnaround period of acceleration, the clock on earth is running much faster than the one on the spaceship. Thus most of the time difference occurrs during the turn-around. To quote the same text "Note this is not the case of two observers each believing the other's clock is slow. Everyone agrees that in an accelerated reference frame the speed of a clock depends on its position and clocks higher "up" run faster."

Anyway, I'm still checking the math on this one, so I reserve the right to change my opinion. It's been a while since I've had to deal with this sort of qual problem question, so I'm rusty. I did recollect this argument though, which is why I was so insistent on why GR was required to fully resolve the twin paradox. More to come.

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"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli

I think that the time dilation under GR is related to the gravitional field. At higher altitude, the G-field is weaker and so there is less time dilation. In an accelerating frame though, the time dilation is uniform throughout.

That is right, as the acceleration due to gravity decreases with distance, down the time dilation effect will also drop off. For a constant acceleration, though that won't be the case. Anyway, I'm still working on this one, so I'll withold further comment for a while. 8)

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"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli