Introduction to Special/General Relativity - Beginner's Question

[Mr. Minnow]

I've recently started reading Brian Greene's The Elegant Universe, the first part of which deals with special and general relativity. For the most part I'm finding it very lucid and accessible: it's aimed at those with little or no specialist training in mathematics or physics, so he keeps the text equation-free and uses various examples to explain the concepts involved. However, the section explaining the contraction of a moving object along its direction of motion is very brief. Here's what Greene says:

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"The preceding discussion reveals that observers see moving clocks ticking more slowly than their own - that is, time is affected by motion. It is a short step to see that motion has an equally dramatic effect on space. Let's return to Slim and Jim on the drag strip. While in the showroom, as we mentioned, Slim had carefully measured the length of his new car with a tape measure. As Slim is speeding along the drag strip, Jim cannot apply this method to measure the length of the car, so he must proceed in an indirect manner. One such approach, as we indicated earlier, is this: Jim starts his stopwatch just when the front bumper of the car reaches him and stops it just as the rear bumper passes. By multiplying the elapsed time by the speed of the car, Jim can determine the car's length.

Using our newfound appreciation of the subtleties of time, we realize that from Slim's perspective he is stationary while Jim is moving, and hence Slim sees Jim's clock as running slow. As a result, Slim realizes that Jim's indirect measurement of the car's length will yield a shorter result than he measured in the showroom, since in Jim's calculation (length equals speed multiplied by elapsed time) Jim measures the elapsed time on a watch that is running slow. If it runs slow, the elapsed time he finds will be less and the result of his calculation will be a shorter length.

Thus Jim will perceive the length of Slim's car, when it is in motion, to be less than its length when measured at rest. This is an example of the general phenomenon that observers perceive a moving object as being shortened along the direction of its motion."

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I think I've understood this. I get the idea that from Slim's perspective, in which he is stationary and Jim is moving, Jim will record a shorter length because his (Jim's) clock is running slow. Here's my question: what if we take Jim's perspective, i.e. Jim is the stationary observer and Slim is moving? In that case, Jim's clock will not be running slow, it will be running normally. So why, from Jim's perspective, does he record a shorter length? I'm guessing that it has something to do with the fact that if Jim is stationary and Slim is moving then Slim is the one whose clock will be running slow - does Jim measure a shorter length because he records less time elapsing on Slim's clock? Jim's calculation is length = speed multiplied by elapsed time, so he would indeed record a shorter length if the elapsed time referred to in that calculation is the time he records elapsing on Slim's slow-moving clock. Greene does talk about Jim making his calculation based on the time elapsed on his own clock though, so maybe I'm wrong.

It seems surprising that Greene has explained the phenomenon of length contraction in his example from one perspective but not the other. Any help gratefully received! 

[Ken B]

It is the same from both perspectives. It is perfectly symmetrical.

If you want a great book, Relativity Visualized by Epstein.

[Mr. Minnow]

It is the same from both perspectives. It is perfectly symmetrical.

OK, so in Slim's perspective:

Slim realises that Jim will measure a shorter length because he sees Jim's clock as running slow (hence the amount of time Jim measures elapsing will be lower).

In Jim's perspective:

Jim measures a shorter length because he sees Slim's clock as running slow (hence the amount of time Jim measures elapsing on Slim's clock will be lower) . If so, the "elapsed time" referred to in Jim's calculation is the time he measures elapsing on Slim's clock - which would make sense, though it would make me wonder why Greene refers to Jim making his calculation based on the time elapsed on his own clock.

If you want a great book, Relativity Visualized by Epstein.

Thanks, seems to be out of print in the UK unfortunately.

[relm1]

Well, I can't say this is a topic I expected to find on this forum.  If your question is why does time slow down as you approach the speed of light, see this video which I thought explained it well: https://www.youtube.com/watch?v=Cx12cEYpEk0

[Parsifal]

Einstein himself wrote a very fine book for non-experts. He conceived the theory in a very intuitive way and his explanations are easy to follow and (of course) insightful.

You should be able to get a kindle edition for free of very cheap. I recall that more than one edition was available, make sure to get one in which the diagrams have been rendered in an acceptable way.  One option is

[asin]B004M8S53U[/asin]

[bwv 1080]

And all the time dilation effects of general relativity prove the earth is 6000 years old.  That light from Andromeda isnt 2.5 million years old, its just time dilated 

http://creation.com/starlight-and-time-a-further-breakthrough

[Parsifal]

There is another way to describe the effect which, at its root, is the same but which I find more intuitive.

Suppose you are measuring the length of your car, you make a mark on your ruler corresponding to the front bumper and you make another mark on your ruler corresponding with the rear bumper. You subtract the two positions and get the length. If the ruler and car are at rest that is straightforward measurement. Assume that you measure the car to be length 10 meters using this method.

Now, what if we try to confirm this when the ruler is at rest but the car is moving forward (to the right). Now we have to be careful to measure the position of the front and rear bumper simultaneously. If we mark the front and rear bumper of a moving car at different times we will not get the correct length.

In special relativity there is a problem with "simultaneously." You can unambiguously define two events as simultaneous if they occur at the same position in space. But if two events occur at different locations, how do you determine if they are "simultaneous?"  It turns out that in special relativity an observer at rest with respect to the ruler and an observer riding in the car will not agree about whether clocks located at different locations along the ruler are synchronized, and therefore whether events occurring at different locations are simultaneous or not.

An observer who has carefully synchronized the clocks that she has placed on the ruler will measure the front and back of the car at what her clocks indicate is the same instant, but the observer riding in the car will say, "no fair, you measured my front bumper first, then measured my rear bumper an instant later, and that's why you come up with a length which less than 10 meters."

It works the other way as well. If the observer riding the car puts clocks on his front and rear bumper and satisfies himself they are synchronized with respect his frame of reference he can try to measure the marks on the ruler, which appears to him to be moving to the left. He will measure the ruler as shorter than 10 meters, and the observer on the ruler will say, "no fair, you measured my 0 meter mark first then measured my 10 meter mark an instant later, and that is why you think it is shorter."

It is not that anything physically contracts. The two ends of the object are still 10 meters apart, but different observers will not agree whether or not the two ends of the object are 10 meters apart at the same time.

[bwv 1080]

A practical example is GPS which depends on both general and special relativity for accuracy:
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.

[The new erato]

It is not that anything physically contracts. The two ends of the object are still 10 meters apart, but different observers will not agree whether or not the two ends of the object are 10 meters apart at the same time.

Good explanation. And it all hinges on the speed of light received by you being constant, independent on whether the source of light is moving towards you or away from you. The consequence is that when travelling at speeds close to the speed of light, ordinary phenomena can only be explained by dimensions contracting or time slowing down, which turns out to be two faces of the same coin....

[Mr. Minnow]

There is another way to describe the effect which, at its root, is the same but which I find more intuitive.

Suppose you are measuring the length of your car, you make a mark on your ruler corresponding to the front bumper and you make another mark on your ruler corresponding with the rear bumper. You subtract the two positions and get the length. If the ruler and car are at rest that is straightforward measurement. Assume that you measure the car to be length 10 meters using this method.

Now, what if we try to confirm this when the ruler is at rest but the car is moving forward (to the right). Now we have to be careful to measure the position of the front and rear bumper simultaneously. If we mark the front and rear bumper of a moving car at different times we will not get the correct length.

In special relativity there is a problem with "simultaneously." You can unambiguously define two events as simultaneous if they occur at the same position in space. But if two events occur at different locations, how do you determine if they are "simultaneous?"  It turns out that in special relativity an observer at rest with respect to the ruler and an observer riding in the car will not agree about whether clocks located at different locations along the ruler are synchronized, and therefore whether events occurring at different locations are simultaneous or not.

An observer who has carefully synchronized the clocks that she has placed on the ruler will measure the front and back of the car at what her clocks indicate is the same instant, but the observer riding in the car will say, "no fair, you measured my front bumper first, then measured my rear bumper an instant later, and that's why you come up with a length which less than 10 meters."

It works the other way as well. If the observer riding the car puts clocks on his front and rear bumper and satisfies himself they are synchronized with respect his frame of reference he can try to measure the marks on the ruler, which appears to him to be moving to the left. He will measure the ruler as shorter than 10 meters, and the observer on the ruler will say, "no fair, you measured my 0 meter mark first then measured my 10 meter mark an instant later, and that is why you think it is shorter."

It is not that anything physically contracts. The two ends of the object are still 10 meters apart, but different observers will not agree whether or not the two ends of the object are 10 meters apart at the same time.

Thanks, that's a good explanation. So let me see if I've got this: if the ruler and clocks are at rest and the car is moving to the right, the car's motion means that the front bumper will register on the ruler first (as seen from the car). The rear bumper then has to "catch up" to be registered on the ruler a short time later. During that interval the rear bumper has moved slightly to the right compared to where it was when the front bumper was registered. Hence the shortened length measured by the observer on the ruler. 

From the other perspective, with the observer on the car putting clocks on each bumper which are synchronised in his frame of reference, it is the ruler which appears to be moving (to the left). The ruler's motion means the observer on the ruler will see the observer on the car register the passing of the 0 meter mark first, with the 10 meter mark having to "catch up" a short time later. During that time the 10 meter mark has moved slightly to the left compared to where it was when the 0 meter mark was registered, so the observer in the car will register a length shorter than 10 metres.

I hope I've got that right!

[Ken B]

Here is an intuition based on a fundamental idea (geometry). You are always moving through spacetime. As measured by any inertial observer you are always moving at the same speed. The trick is you can either move through time (and not through space)  or through a combination of both. (light and a few other things move through space not through time.) But you always move at the same speed in spacetime. In your proper reference frame you move through time, as you measure it. Imagine that you strike a match and 10 seconds later by your watch you blow it out. In your frame of reference you have not moved in space so all your movement is in time as you measure it. the time elapsed you measure is 10 seconds. You have moved a total of 10 "seconds", and every inertial observer agrees on that. What do I see if you are moving in my frame of reference? I see you strike the match and I see you blow out the match. I see that you have moved a few yards of space in the meantiime so you must have moved less than 10 "seconds" on your clock as I measure it. Your clock runs slow.

It's symmetrical. You see my clock run slow by the same argument.

This glosses over an important point or three, but might help as a starter to see what is happening.

This also tells you why you cannot go faster than light if you think it through.

[Mr. Minnow]

Here is an intuition based on a fundamental idea (geometry). You are always moving through spacetime. As measured by any inertial observer you are always moving at the same speed. The trick is you can either move through time (and not through space)  or through a combination of both. (light and a few other things move through space not through time.) But you always move at the same speed in spacetime. In your proper reference frame you move through time, as you measure it. Imagine that you strike a match and 10 seconds later by your watch you blow it out. In your frame of reference you have not moved in space so all your movement is in time as you measure it. the time elapsed you measure is 10 seconds. You have moved a total of 10 "seconds", and every inertial observer agrees on that. What do I see if you are moving in my frame of reference? I see you strike the match and I see you blow out the match. I see that you have moved a few yards of space in the meantiime so you must have moved less than 10 "seconds" on your clock as I measure it. Your clock runs slow.

It's symmetrical. You see my clock run slow by the same argument.

This glosses over an important point or three, but might help as a starter to see what is happening.

This also tells you why you cannot go faster than light if you think it through.

I think I get the basic idea, I'm just trying to apply it to the specific details of Greene's example that I mentioned at the start of the thread. I understand that in his example, from Slim's perspective the reason Jim measures a shorter length is the fact that Jim's clock is running slow (as Jim is moving); so, from Slim's point of view the elapsed time on Jim's clock is lower and hence Jim's calculation will produce a shorter length.

But from Jim's perspective that obviously can't be the reason he measures a shorter length, since from his point of view his clock is running normally and it is Slim's that is running slow, since Slim is moving. So what I was trying to pin down is the reason, from Jim's perspective, that he measures a shorter length (this is the part of his example that Greene doesn't explain).

It must presumably be connected to the fact that from Jim's perspective Slim's clock is running slow. Jim's calculation is length = speed multiplied by elapsed time, so I'm assuming that the "elapsed time" in that calculation must be the amount of time Jim records elapsing on Slim's slow moving clock. Jim's clock is running normally, so the "elapsed time" part of his calculation cannot (I assume) refer to the amount of time he records elapsing on his own clock, as that would not measure a shorter amount of elapsed time, and therefore would not result in measuring a shorter length.

Sorry if that seems a bit long-winded, but that's how I interpreted it.

[XB-70 Valkyrie]

I read that book ages ago, and while Greene is certainly a very good writer, you should keep in mind that theory (-ies) of everything, string theory, etc., have transformed dramatically in the last decade or so, from what I understand. Sadly, I don't have the time to follow the field as I once did.

From what I understand, string theory fell out of favor with some because it makes predictions that cannot be tested empirically, which pushes it outside the realm of science. The discovery of the Higgs Boson likely also shifts the picture a great deal. You might look for one of Greene's more recent titles, or the book From Eternity to Here. Dipping into the peer-reviewed literature is also an option--look for review papers geared to non-specialists.

[Jo498]

But the "core", i.e. special and general relativity are still established and not in immediate danger of being revised.

The problem with string/brane/whatever theories being too remote from possible data has been recognized for quite a while. (Actually there were a few prominent critics, such as Glashow, from very early on.)
String theories would be "deeper" foundations of the current standard model + Higgs that would probably not be revised substantially if any of them became established.

As far as I understand the more pressing trouble is that CERN has not really found anything besides the Higgs. No superpartners or other stuff that would make any of the many "conservative" extensions or amendments (like Supersymmetry) of the standard model more likely have been found. So from a practical view concerning physics that is within the range of the actual LHC (and similar) experiments, the "standard model" is still the standard and anything beyond that very shaky in comparison. Therefore I see no great loss if for laymen the focus is mainly on the standard model although it is basically 40 years old.

[Ken B]

Therefore I see no great loss if for laymen ...

Well, aside from the 100 trillion billion dollars they spent on it.

[71 dB]

Mr. Minnow:

Imagine sitting inside a moving train with a mirror ceiling. You point a laser up. You "see" the beam going up at the speed of light (~3*10^8 m/s) and coming back down to you at the same speed. Nothing special. Now, someone standing next to your train looks at your laser beam while you move relative to him/her. He/she seems the photons of the beam move up AND forward and down AND forward forming a triangle. The distance he/she sees the beam move is longer than what you see (twice the distance between your laser and the ceiling). Since the speed of light is the same for everyone, he/she must see the light of your laser moving straight up and down slower than the speed of light, because the forward movement adds some speed so that the combined speed is ~3*10^8 m/s. That's means he/she sees your time going slower. If you moved at the speed of light relative to him/her*, your forward movement would be "all", and he/she wouldn't see the beam move up or down at all meaning your time would have "frozen" to him/her.

The world as far as we know is 4-dimensional (+ 7 or something inner dimensions irrelevant here). Because we always move VERY slowly in relation to objects in our relevant environment, we always see certain kind of 3D-projections of the 4-dimensional reality. It makes us believe there is just 3 dimensions and time is not related. We don't "see" that the sun we see is the sun 8 minutes "ago". We don't see how the light from the stars on the sky is many years old. What we see we think is "now" even if we are smart enough to know better. When you start moving faster and faster, the 3-dimensional projection you see changes. It's like how the shape of a shadow changes when you rotate the object creating the shadow.

* Impossible, but let's imagine it was possible.

[drogulus]