Layman in search of help understanding relativity

[noscience123]

I'm an adult in the finance industry with no science background, and I'd like some help understanding relativity. I'm reading Walter Isaacson's biography of Einstein, and while I know it's not the point of the book, I can't get my head around the passages concerning relativity and it's really bugging me. I've researched on the web and all of the sites give the same few analogies, which I understand, but it's still not coming together for me. I'm hoping if I ask a pointed question or two that someone might be able to help me clear up my misconceptions.

So I understand the lightning strikes the front and back of the train metaphor. The lightning truly looks simultaneous to the man on the platform, but to the man on the train it looks like the lightning hits the front of the train first. But then they talk about the clock on the train moving slower than the clock on the platform and I get lost. So here's a hypothetical - let's say the man on the platform and the man on the train have walkie-talkies. The man on the platform reads off each second as it passes on the platform clock. For the man on the train, does it sound like the man on the platform is counting at the right pace? (i.e. truly a second passes between each number) and does the pace of the seconds he hears from the platform man match the second hand on the clock he sees inside the train?

Any help answering - or if I am on the wrong track (no pun intended), suggesting another way to look at it altogether - would be greatly appreciated.

 

[Antiphon]

The man in the train hears the man on the platform counting time at a slower rate than his own clock.

The man on the platform hears the man in the train counting time more slowly than his own clock is running.

Anyone moving relative to you has their clock appearing to run slower, hence the "relativity."

 

[Ich]

Don't know if you want such details, but actually the man on the train hears the man on the platform counting at a higher rate as he approaches, and at a slower rats as he recedes. That's called "Doppler effect" and and is due to the ever changing signal travel times between both.
Only after mathematically correcting for the signal travel time will he conclude (not directly observe or hear) that the platform clock runs at a slower rate than his.

 

[noscience123]

Ok, thanks. One of you mentioned signal time - I guess I have a follow-on then. Pretend you could somehow have magic walkie-talkies where nothing has to travel between them - they just communicate instantaneously - would it then seem like they are counting time at the same pace? And relating back to relativity - I guess I'm wondering, is it only the travel time between the two that makes it seem like their clocks move at different speeds? i.e. if you could somehow 'know' both clocks at once (forget about light traveling - pretend you somehow could just know what time they read) would this effect go away? sorry for the weird questions, but it just seems like this is an illusion created because light has to travel and that you think these effects exist because you haven't received the correct light yet, if that makes sense.

 

[Ich]

Pretend you could somehow have magic walkie-talkies where nothing has to travel between them - they just communicate instantaneously - would it then seem like they are counting time at the same pace?

Relativity is deeply inconsistent with "instantaneous" communication. If this were possible, the whole theory were garbage and had nothing to say on clock rates and the like.

And relating back to relativity - I guess I'm wondering, is it only the travel time between the two that makes it seem like their clocks move at different speeds?

As I said: no. After correcting for light travel times, time dilation is what remains.

There is this "relativity of simultaneity", which means that different observers have different notions of which distant events are happening "now". This is absolutely crucial. If you pretend that there is only one well defined "now" (a prerequesite of instantaneous communication), you kill the theory.

 

[noscience123]

Ok, great - that is what I kinda suspected. This is very helpful. Now my last follow-up (I hope) - this leads me to confusion about the next analogy, the boy who travels near light speed away from Earth and then back and is younger than his twin he left behind. If you could theoretically communicate instantaneously, the two could use the magic walkie-talkies and count off seconds simultaneously from the time the space twin leaves until the time he returns. And there would be the same number of simultaneous seconds that elapse, since their communication is instantaneous. But then how is it that the space boy is younger upon returning? That's the part that I'm still missing.

 

[bapowell]

Ok, great - that is what I kinda suspected. This is very helpful. Now my last follow-up (I hope) - this leads me to confusion about the next analogy, the boy who travels near light speed away from Earth and then back and is younger than his twin he left behind. If you could theoretically communicate instantaneously, the two could use the magic walkie-talkies and count off seconds simultaneously from the time the space twin leaves until the time he returns. And there would be the same number of simultaneous seconds that elapse, since their communication is instantaneous. But then how is it that the space boy is younger upon returning? That's the part that I'm still missing.

You're right to be confused; this is the famous twin paradox! Of course, twin A who is moving relative to twin B, perceives twin B's clock to be ticking slow. And also of course, twin B who is moving relative to twin A, perceives twin A's clock to be ticking slow. There is a perfect symmetry to this problem. So...how does this symmetry get broken, manifested as one twin aging more slowly than the other??

It has to do with the fact that the twin who departs earth, in order to later return to earth, must at some point turn around. You may have read that special relativity applies only to inertial reference frames -- those in which observers move at constant velocities. In turning around, one must accelerate -- this breaks the symmetry. I'm not sure if this will be helpful, but here's a spacetime diagram from the wikipedia Twin Paradox page:

http://upload.wikimedia.org/wikipedia/commons/c/ce/Twin_Paradox_Minkowski_Diagram.svg"

It's all about simultaneity. The change of direction of the traveling twin changes the planes of simultaneity so that the age of the stationary twin 'jumps' at the moment of turn around. The article does a good job of discussing this, so perhaps I'll defer to it at this point.

 

[Ich]

And there would be the same number of simultaneous seconds that elapse, since their communication is instantaneous.

If we assume that all clocks and processes follow this universal time: Yes. But experiments show that this is not the case.
One could assume that there is such a universal time, but all clocks and processed are somehow slowed down depending on absolute velocity. In such a theory you could have one of the twins actually aging slower. If this happens in a very fine-tuned way, with the length of objects also changing depending on velocity and direction, such a theory http://en.wikipedia.org/wiki/Lorentz_ether_theory" makes the same observational predictions as Special Relativity.
Actually, it is this interpretation that you are likely to get taught in school or read in popular papers. You have clocks slowing down there and meter sticks contracting, and instantaneous communication is not a problem. But the theory does not conform to the principle of relativity. Reciprocal time dilation would be a real paradox in such a theory. I believe that the mixing up of LET with SR in the public perception is true reason of the difficulties many people have with SR.

But then how is it that the space boy is younger upon returning?

You can take the easy route with LET and simply claim that one of the twins is really moving, and that his clocks (and he/she) have slowed down during the trip. But this viewpoint loses all its charm when faced with the fact that this "real motion" is undetectable.

SR is harder at first glance. There, space and time are interchangeable to some degree. The theory reduces to some simple (if unintuitive) geometry, where the length of a path through spacetime is the elapsed proper time. It's obvious that different paths have different length.
For example, stay-at-home's path is a straight line, while the traveling twin's path is bent.

There are thousands of threads about the twin paradox, maybe you want to read some and then come back with questions.

 

[noscience123]

I think you both gave me credit for understanding more than I do in your responses. listenting to you both made me realize I get even less than I did. I did go back and look at the twin paradox and time dilation threads, and the wikipedia, though the wikipedia lost me quickly (and I should be working, but this problem has engrossed me). I think this is just too hard to get without understanding some of the math, which I am never going to get. So I'm going to present one last scenario and see if you can tell me where my logic is off. If I don't get it then, I'll leave you all alone.

Twin A leaves on spaceship traveling at half of light speed and he passes the spot one light year from earth, right as his clock strikes 2 years after he left. by the time the light from his clock hits earth, twin B on Earth will see '2', but twin B will have aged 3 years. At 2 light years away, twin A's clock reads 4, and its light reaches Earth when twin B has aged 6 years. Twin A turns the spaceship around right at 2 light years away (which takes minimal time) and heads back. When twin A is back to one light year away from earth, his clock reads 6 light years after he left, and the light from that clock reaches Earth when twin B is 7 years older. Twin A is half a light year away at that point. He keeps going and finally, twin A reaches Earth when his clock reads 8. Twin B has aged 8 years as well, which goes against the theory. There's obviously a flaw, but I can't figure it out.

Again, I think without getting into the real math of velocity and space travel, you won't be able to give me an answer, but I thought I'd give it one more shot. thanks for your help.

 

[noscience123]

Disregard the last post... I just read in another thread that the speed of light also depends on one's frame of reference. I'm giving up now. I think I wasn't meant to be a physicist :)

 

[JesseM]

Disregard the last post... I just read in another thread that the speed of light also depends on one's frame of reference. I'm giving up now. I think I wasn't meant to be a physicist :)

Which thread did you read that? The speed of light is the same in every inertial reference frame (a frame where every point is moving in a straight line at constant speed, not accelerating).

 

[noscience123]

I don't recall. Maybe that's not a problem then. What are your thoughts on the above twin timeline? thx

 

[IcedEcliptic]

Relativity of simultaneity, there are excellent threads on it to be found here, complete with the classic twin-paradox spacetime diagram.

[PLAIN]http://web.comhem.se/~u87325397/Twins.PNG

 

[JesseM]

Twin A leaves on spaceship traveling at half of light speed and he passes the spot one light year from earth, right as his clock strikes 2 years after he left.

One light year from Earth in which frame? Keep in mind that because of length contraction, the distance between two objects which are at rest relative to each other (like two ends of a measuring-rod, or Earth and another planet at rest relative to the Earth) will be shorter in the frame of an observer moving relative to these objects than it is in the frame of an observer at rest relative to them. If you want the distance to be one light year in twin A's frame, then the distance must be greater in the frame of Earth and the planet twin A is traveling to. Specifically, if twin A is traveling at 0.5c, then he sees the distance shrunk by a factor of $$\sqrt{1 - 0.5^2}$$ = 0.86603; so if the distance for him is one light year, the distance in Earth's frame must be 1/0.86603 = 1.1547 light years.

by the time the light from his clock hits earth, twin B on Earth will see '2', but twin B will have aged 3 years.

No. First of all you need to distinguish the time an event happens in twin B's frame from the time twin B actually sees the light from an event--the time coordinate of the event is based on subtracting off the light travel time, so if I see an event in 2013 which occurred 3 light-years away in my frame, then I must assign the event a time coordinate of 2013-3=2010. In your example, the travel time is not 1 year but 1.1547 light years, so twin B will see the light from twin A's clock reading '2' 1.1547 years after whatever time coordinate twin B actually assigns to the event of twin A's clock reading '2'. But twin B does not say this event happened when twin B's clock also read '2'--if it did, then there would be no genuine time dilation, and any difference in ages would be purely an optical effect! According to the time dilation equation, the time for a clock which is moving at speed v to elapse a time of T should be stretched out (dilated) to a time of $$T/\sqrt{1 - v^2/c^2}$$ in my frame. So in B's frame, the time for A's clock to elapse 2 years is stretched out to $$2/\sqrt{1 - 0.5^2}$$ = 2/0.86603 = 2.3094 years. So in B's frame, A's clock didn't read '2' until 2.3094 years after A's departure, and then it took an additional 1.1547 years for the light from this event to reach B, so that B has aged 2.3094 + 1.1547 = 3.4641 years by the time he sees the image of B's clock reading '2'.

At 2 light years away, twin A's clock reads 4, and its light reaches Earth when twin B has aged 6 years.

When A is at a distance of 2 light years in his own rest frame, his clock does read 4, but he's at a distance of 2/0.86603 = 2.3094 light years in twin B's rest frame due to length contraction, and by this time B has aged 4/0.86603 = 4.6188 years due to time dilation (you could also just take the distance of 2.3094 light years and divide by the speed of 0.5c to get a time of 4.6188 years in B's frame). Then the light from this event takes an additional 2.3094 years to reach B, so B sees it when his age is 4.6188 + 2.3094 = 6.9282 years.

Twin A turns the spaceship around right at 2 light years away (which takes minimal time) and heads back. When twin A is back to one light year away from earth, his clock reads 6 light years after he left, and the light from that clock reaches Earth when twin B is 7 years older.

When twin A is 1 light year away again in his frame, he's again 1.1547 light years away in B's frame, and B has aged 6/0.86603 = 6.9282 years. Then the light from this event takes another 1.1547 years to reach B, so B sees this when he has aged 6.9282 + 1.1547 = 8.0829 years.

Twin A is half a light year away at that point. He keeps going and finally, twin A reaches Earth when his clock reads 8. Twin B has aged 8 years as well, which goes against the theory. There's obviously a flaw, but I can't figure it out.

Again, time dilation is not just an optical effect due to light delays, it's what you're left with after you subtract out the light delays to find the "real" time an event happened in your frame (like my example of seeing an event 3 light-years away in 2013 and concluding it 'really' happened in 2010 in your frame). When twin A returns to Earth having aged 8 years, twin B will have aged 8/0.86603 = 9.2376 years.

 

[noscience123]

Thanks for the very thorough response. that makes it a lot clearer. So this time dilation - how does that happen? (tongue in cheek) I guess that's what makes this so hard, is that an untrained mind is so reluctant to believe that two organisms could take different paths through space and arrive at the same point in the future and their cells would have biologically aged different amounts.

 

[tiny-tim]

Hi noscience123!

… If you could theoretically communicate instantaneously, the two could use the magic walkie-talkies and count off seconds simultaneously from the time the space twin leaves until the time he returns…

I'm not sure if this has been precisely answered, but (even if instantaneous communication were possible) they would not be able to agree on what was instantaneous … if A sending a message and B receiving it are instantaneous as regarded by A, they are not instantaneous as regarded by B.

 

[JesseM]

Thanks for the very thorough response. that makes it a lot clearer. So this time dilation - how does that happen? (tongue in cheek) I guess that's what makes this so hard, is that an untrained mind is so reluctant to believe that two organisms could take different paths through space and arrive at the same point in the future and their cells would have biologically aged different amounts.

Well, you can derive time dilation from the two postulates of relativity--the first postulate saying that the laws of physics work the same in all inertial reference frames, the second postulate saying that the speed of light is the same in all inertial reference frames--but then you still have the question of why the postulates are valid...physics can't really address the ultimate "why" questions, only tell you how things work. One analogy that may be helpful in thinking about time dilation is distance along a path in space; just as two cars can take different routes between a pair of points A and B and their odometers will record different elapsed distances, with the straight-line path between A and B always being the one with the smallest odometer distance, so it is also true that different ships can take different routes between a pair of points A and B in space and time, and their clocks will show different elapsed times, with the straight-line (and constant speed) path between A and B always being the one with the greatest elapsed time. In fact there is even a spacetime analogue of the pythagorean theorem for distance in space (and the fact that the equation is similar but not quite the same explains why a straight-line path has the longest time rather than the shortest), see my post #114 on this thread for details.

 

[noscience123]

Very interesting about the space-time pythagorean relationship. So counterintuitive that the constant velocity line takes the longest time. thanks again for everyone's help!

 

[IcedEcliptic]

Very interesting about the space-time pythagorean relationship. So counterintuitive that the constant velocity line takes the longest time. thanks again for everyone's help!

Hey, welcome to PF, and a fine entry too.

 

[jamesmo]

I guess I am a bottom up kinda physicist. We have to start with the observation that the speed of light is the same, regardless of the velocity of the observer. Time dilation, length contract, any measurement of length or time must conserve this singular fact. The mathematical calculation of time dilation is almost beside the point. It is easier just to remember if you speed up (distance travelled/per unit time), your clock has to slow down and lengths must contract to conserve the speed of light. The name, relativity, is almost a misnomer. Galilean relativity has every velocity (light, trains, falling stones) being a simple problem of adding the vector velocities to get one speed relative to another. Special relativity does a similar physics, this time in the face of the dreadful fact that at the end of the day, the speed of light must be constant regardless of how fast an observer is going when they look at it. Therefore length and times have to change to preserve the core tenant. General Relativity takes this idea one step further in considering accelerate frames, in particular the case of gravity.

Why the speed of light is constant, is above my pay-grade.

 

[sponsoredwalk]

I've read Isaacson's book & it's good, I had a small bit of respect for him until I found out that he wrote an 'admiring' book about the criminal Henry Kissinger.

So I understand the lightning strikes the front and back of the train metaphor. The lightning truly looks simultaneous to the man on the platform, but to the man on the train it looks like the lightning hits the front of the train first. But then they talk about the clock on the train moving slower than the clock on the platform and I get lost. So here's a hypothetical - let's say the man on the platform and the man on the train have walkie-talkies. The man on the platform reads off each second as it passes on the platform clock. For the man on the train, does it sound like the man on the platform is counting at the right pace? (i.e. truly a second passes between each number) and does the pace of the seconds he hears from the platform man match the second hand on the clock he sees inside the train?

http://www.youtube.com/watch?v=wteiuxyqtoM&feature=related

I hope this video willl illuminate things for you.

Youtube has a lot of helpful visualizations on special relativity that are worth your time if your interested.

Also, http://video.google.com/videoplay?docid=-2213602821869460358#docid=-6328514962912264988 video will give you a bit of insight into the math using some algebra & show you the pythagorean theorem's involvement clearly.

 

[AdVen]

I'm an adult in the finance industry with no science background, and I'd like some help understanding relativity. I'm reading Walter Isaacson's biography of Einstein, and while I know it's not the point of the book, I can't get my head around the passages concerning relativity and it's really bugging me. I've researched on the web and all of the sites give the same few analogies, which I understand, but it's still not coming together for me. I'm hoping if I ask a pointed question or two that someone might be able to help me clear up my misconceptions.

So I understand the lightning strikes the front and back of the train metaphor. The lightning truly looks simultaneous to the man on the platform, but to the man on the train it looks like the lightning hits the front of the train first. But then they talk about the clock on the train moving slower than the clock on the platform and I get lost. So here's a hypothetical - let's say the man on the platform and the man on the train have walkie-talkies. The man on the platform reads off each second as it passes on the platform clock. For the man on the train, does it sound like the man on the platform is counting at the right pace? (i.e. truly a second passes between each number) and does the pace of the seconds he hears from the platform man match the second hand on the clock he sees inside the train?

Any help answering - or if I am on the wrong track (no pun intended), suggesting another way to look at it altogether - would be greatly appreciated.

I think you should start with the beginning. The beginning of special relativity is the derivation of the Lorentz transformation. You can find the derivation of the Lorentz transformation for the layman on

http://www.socsci.ru.nl/~advdv/EinsteinBold.htm

but that text is in Dutch. If you want me to translate the text, please, let me know.