Not Understanding Time Dilation.

[The New Guy]

Hey there, guys. I’m kind of new to the whole physics thing, but I am starting on a quest to try and learn as much about how this universe works as I can. I am currently working on developing a good understanding of special and general relativity. I am not overly math-competent, so I have been sticking to the conceptual area of relativity as much as I possibly can. I have done quite a bit of studying on the subject, and I have most of the concepts at least “memorized.” I don’t necessarily “understand,” however, so don’t feel too shocked if I say a few things that make you scratch you heads.

In trying to fully comprehend special relativity, the biggest road block I’ve hit is this: I don’t understand where the physical slowing of time for objects in relative motion comes into play in preserving the speed of light in all reference frames. This is what I am hoping you guys can answer for me.

I have seen some examples. The most common one is the “light clock,” a clock where a beam of light bounces back and forth between two panels, and each period is one “tick” of the clock. To an observer who is stationary relative to the light clock, the light bounces back and forth between the panels along the shortest possible path. However, when the clock is put into near-light-speed-motion relative to the observer, the light has to travel a longer, diagonal path between the panels due to the fact that the clock itself has changed position. When in relative motion with its observer, the clock ticks more slowly. I understand this, and it makes perfect sense. However, what I am having trouble understanding is why it has to be that this applies to all things, and not just the light clock. In other words, I don’t understand why an hour glass takes longer than an hour to cycle through when viewed by an observer in relative motion, or why a person can take a high-speed journey for 100 years and come back only 50 years aged.

I know I am wrong here, but it seems to me like relative simultaneity and length contraction would be enough to preserve the speed of light without any time dilation in addition. For example, a person is standing stationary with respect to two lightning rods, one that is 1,000,000 miles to his left, and another that is 1,000,000 miles to his right, and he sees two simultaneous lightning strikes. Meanwhile, I am whizzing past him in a rocket from left to right, traveling at near the speed of light. I fly into the wave of light coming from the lightning strike on the right, and the one from the left has to chase me down from behind. I see the lightning strike that I am flying towards before I see the lightning strike that I am flying away from. Both lightning strikes occurred the same distance from me, and advanced towards me at exactly speed c, and D=RT, so that means that the lightning strike that I was flying towards actually happened first, and the speed of light is preserved. I also understand that there is a length contraction in there, but I won’t go into the details of that. What I don’t see is where each observer viewing the other observer’s clock as running slowly comes into play here. It seems as though the speed of light is already preserved, and the laws of physics are the same in both reference frames, and it is mission accomplished. Where is my thinking off here?

I’m hoping you guys can give me a mental picture of why time dilation has to be, so that I can truly understand this stuff. I understand that it might be impossible without getting mathematically involved, so feel free to just say so if it is.

Thanks a bunch!

 

[ghwellsjr]

If you agree that the ruler that the traveler is carrying with him is length contracted along the direction of motion, then when he measures the speed of light using that ruler to measure the distance the light travels during some period of time, he will get the wrong answer unless his clock is also ticking at a slower rate.

 

[The New Guy]

Thanks for the answer. I do have one question though. Suppose I am standing on the ground with a 10 light second ruler to my left. A spaceship with an identical ruler hanging off the back of his ship then flies past me from left to right at near the speed of light, and at the precise time that he is alongside me, he fires a laser backwards. The laser beam has to travel at speed c relative to me and at speed c relative to him at the same time. Since he is moving relative to me, I see his 10 light second ruler as being scrunched, maybe only 5 light seconds, plus he is advancing away from the laser beam.

10 seconds pass on my clock, and the laser beam is right at the end of my ruler. Meanwhile, the same beam of light is far beyond the end of the ruler that the spaceship had been dragging behind him. Let’s say the light traveled 25 light seconds away from him by his measurements, in the same amount of time that it took to travel 10 light seconds away from me. This would mean that 25 seconds must have passed on his clock, and time for him must be passing faster than for me. What is wrong with this picture I painted? I understand that I have to view his clock as ticking slower than mine.

Sorry for the dumb questions, but I am new to this, and having some trouble understanding what is going on.

 

[Janus]

Thanks for the answer. I do have one question though. Suppose I am standing on the ground with a 10 light second ruler to my left. A spaceship with an identical ruler hanging off the back of his ship then flies past me from left to right at near the speed of light, and at the precise time that he is alongside me, he fires a laser backwards. The laser beam has to travel at speed c relative to me and at speed c relative to him at the same time. Since he is moving relative to me, I see his 10 light second ruler as being scrunched, maybe only 5 light seconds, plus he is advancing away from the laser beam.

10 seconds pass on my clock, and the laser beam is right at the end of my ruler. Meanwhile, the same beam of light is far beyond the end of the ruler that the spaceship had been dragging behind him. Let’s say the light traveled 25 light seconds away from him by his measurements, in the same amount of time that it took to travel 10 light seconds away from me. This would mean that 25 seconds must have passed on his clock, and time for him must be passing faster than for me. What is wrong with this picture I painted? I understand that I have to view his clock as ticking slower than mine.

Sorry for the dumb questions, but I am new to this, and having some trouble understanding what is going on.

This deals with what is known as the Relativity of Simultaneity. Imagine that your spaceship also has a 10 light second ruler extending in front of Him. according to him, his light pulse reaches the ends of both rulers at the same time. According to you however, the light will reach the end of the trailing ruler first and then the end of the leading ruler. IOW, Events that are simultaneous in one frame will not be so in the other and vice-versa.

 

[pervect]

and at the precise time that he is alongside me, he fires a laser backwards.

I very much suspect that you're having the usual problem with the relativity of simultaneity. But it's a bit hard to interpret your scenario without a space-time diagram. Furthtermore, there's a good chance that drawing up the space-time diagram would help you to clear up your confusion.

The basics of drawing a space-time diagram are simple: chose a scale such that light always moves at a 45 degree angle on the space-time diagram.

Time goes in the vertical direction, so non-moving objects on the space-time diagram are represented with vertical lines, as below.

Moving objects always move less than 'c', so they tilt slightly to the left or right, but never as much as 45 degrees.

To actually measure lengths and time intervals, use 3/4/5 triangles, and remember that the lorentz interval is the square of the time or distance interval and is equal to $| \Delta T^2 - \Delta X^2 |$, so the distance between a point at (t=0,x=0) and (t=4,x=5) is sqrt(5^2 - 4^2) = 3, the distance being space-like.

Finally, and this is the important point - and the main motivation for using the space-time diagrams. Events that are simultaneous are connected by lines of simultaneity, but the slope of the line depends on the observer.

If you aren't familiar with how to draw lines of simultaneity, you can create them from the Einstein midpoint definition, and it's a worthwhile exercise.

To wit - in the stationary frame, you need the worldline of three stationary observers, one is the "midpoint". At some time, the midpoint observer emits a flash of light, we know it arrives "at the same time" by definition on the other two worldlines. The result looks like this - it's no surprise, A and B are two simultaneous events, the thin red line is the "line of simultaneity".

But in the moving frame it looks like this. Again, we use the notion of synchronizing clocks by emitting a light pulse from the co-moving midpoint observer, we know that the signal received from the midpoint arrives "at the same time" in the moving frame.https://www.physicsforums.com/attachment.php?attachmentid=37926&stc=1&d=1313090496

So, when you talk about two events that occur "at the same time", if they are separated by any distance, you need to pick the right line. The concept of "simultaneity" for the stationary observer is a different concept than that of the moving observer, i.e. it depends on the frame.

If you draw everything perfectly to scale, you'll find that the angle between the lines of simultaneity of the moving and stationary observers is the same as the angle between the wordlinles of the moving and stationary observers.

 

[The New Guy]

Once again, thanks for the answers. I feel like I am starting to get a better idea of how relative time, simultaneity, and space work together to preserve the speed of light from all reference frames. However, as can be expected from a confused new guy, your answers lead to more questions.

The question I have now leads somewhat back to my original question, and it is: if relative simultaneity corrects to preserve the speed of light simply by saying that two things that happen simultaneously for one person will not happen simultaneously for somebody in relative motion, why is it that time dilation is a necessary thing? I guess what I am getting out of this is that the relativity of simultaneous events is what actually preserves the speed of light in all reference frames, and that length contraction is a consequence of relative simultaneity, and that time dilation is a consequence of length contraction, so to speak . . . Am I even close here?

 

[nitsuj]

Once again, thanks for the answers. I feel like I am starting to get a better idea of how relative time, simultaneity, and space work together to preserve the speed of light from all reference frames. However, as can be expected from a confused new guy, your answers lead to more questions.

The question I have now leads somewhat back to my original question, and it is: if relative simultaneity corrects to preserve the speed of light simply by saying that two things that happen simultaneously for one person will not happen simultaneously for somebody in relative motion, why is it that time dilation is a necessary thing? I guess what I am getting out of this is that the relativity of simultaneous events is what actually preserves the speed of light in all reference frames, and that length contraction is a consequence of relative simultaneity, and that time dilation is a consequence of length contraction, so to speak . . . Am I even close here?

"Relative simultaneity" is observed because of dilated time and contracted lengths. I would suspect it can't be said one is a "consequence" of the other, they are mutually inclusive.

time dilation / length contraction is a consequence of c being constant, which maybe a result of spacetime properties.

 

[ghwellsjr]

Thanks for the answer. I do have one question though. Suppose I am standing on the ground with a 10 light second ruler to my left. A spaceship with an identical ruler hanging off the back of his ship then flies past me from left to right at near the speed of light, and at the precise time that he is alongside me, he fires a laser backwards. The laser beam has to travel at speed c relative to me and at speed c relative to him at the same time. Since he is moving relative to me, I see his 10 light second ruler as being scrunched, maybe only 5 light seconds, plus he is advancing away from the laser beam.

10 seconds pass on my clock, and the laser beam is right at the end of my ruler. Meanwhile, the same beam of light is far beyond the end of the ruler that the spaceship had been dragging behind him. Let’s say the light traveled 25 light seconds away from him by his measurements, in the same amount of time that it took to travel 10 light seconds away from me. This would mean that 25 seconds must have passed on his clock, and time for him must be passing faster than for me. What is wrong with this picture I painted? I understand that I have to view his clock as ticking slower than mine.

Sorry for the dumb questions, but I am new to this, and having some trouble understanding what is going on.

Once again, thanks for the answers. I feel like I am starting to get a better idea of how relative time, simultaneity, and space work together to preserve the speed of light from all reference frames. However, as can be expected from a confused new guy, your answers lead to more questions.

The question I have now leads somewhat back to my original question, and it is: if relative simultaneity corrects to preserve the speed of light simply by saying that two things that happen simultaneously for one person will not happen simultaneously for somebody in relative motion, why is it that time dilation is a necessary thing? I guess what I am getting out of this is that the relativity of simultaneous events is what actually preserves the speed of light in all reference frames, and that length contraction is a consequence of relative simultaneity, and that time dilation is a consequence of length contraction, so to speak . . . Am I even close here?

You need all three: time dilation, length contraction and relativity of simultaneity. Let me work our your problem in a way that may make it obvious to you.

You stated you have a ruler 10 light seconds long so that when the laser fires, it will take 10seconds for the light to get to the end. However, you cannot see that happening. What you need to do is put a mirror at the end of your ruler so that the light can be reflected back to you and then you will measure 20 seconds elapsing on your watch, confirming that the light did indeed travel the 20 light seconds in 20 seconds.

Now the guy on the spaceship has a similar mirror on the end of his ruler which you say is scunched down to 5 light seconds. You can work the Lorentz factor equation backwards to determine that he is traveling at 86.6%c, correct?

Now if he is traveling at 86.6%c to the right, his mirror is also traveling at that same speed, correct? So now it won't be too hard to figure out how long it will take for the laser beam traveling to the left at c to meet the mirror traveling to the right at 0.866c. It's a simple ratio and it turns out to be 2.68 seconds. Can you figure that out? This also means that the mirror and the spaceship have traveled 2.32 light seconds to the right.

Next we notice that the laser beam is changing direction and the difference in speed between the laser beam and the mirror tells the relative speed between them and that is 0.134c, correct? Now at this speed, the laser beam has to travel 5 light seconds to get to the other end of the ruler and that will take 37.31 seconds, correct? And that is when the guy on the spaceship sees the return laser flash just like you did on the ground. The total elapsed time for him, according to ground time, is 39.99 seconds, but according to him, since his clock is running at half speed is just about 20 seconds, the same as you measured. (The slight error is caused by rounding off the numbers.)

Remember, he thinks his ruler is 10 light-seconds long, so his measurement of the speed of light is the same as yours.

I think you can see the parts that length contraction and time dilation play in this analysis. Simultaneity has to do with the fact that for you, the two halves of the round trip for the laser beam took the same time but as far as you are concerned they were way different for the spaceship guy. If we had done the analysis from his point of view, he would say that the two halves were equal for his ruler and mirror but yours were the ones that were way different.

One last thing: we can calculate how much farther the spaceship had to travel before the reflected laser beam was detected and that is 32.31 light seconds for a total of 34.62 light seconds which is the distance the spaceship traveled in 40 seconds (according to you) at 86.6%c (ignoring round off errrors).

I'm not sure where you got the 25 seconds or why you thought time must be progressing faster for him but hopefully this explanation will clear everything up for you.

 

[The New Guy]

You know, ghwellsjr, I think you may have totally solved my confusion, but not in the way that you expected to solve my confusion. Let me explain. When you stated “You stated you have a ruler 10 light seconds long so that when the laser fires, it will take 10seconds for the light to get to the end. However, you cannot see that happening. What you need to do is put a mirror at the end of your ruler so that the light can be reflected back to you and then you will measure 20 seconds elapsing on your watch, confirming that the light did indeed travel the 20 light seconds in 20 seconds.” you cleared up a lot for me. For whatever crazy reason, I had it in my head that where you see that beam of light, that is where it actually is. I totally neglected the fact that when you are talking about light, you are always talking in terms of round trip. When you see light someplace, you don’t actually see it there. You see it when it comes back to you. As it turns out, my entire problem had nothing to do with relativity. It was actually a simple issue with the nature of light that classical mechanics could have, and did, predict.

When you think it terms of the round trip, it doesn’t matter if the spaceship that you are observing from a distance is traveling towards an oncoming beam of light, or if it is running away from beam of light that is chasing it. Either way, you (on the ground) witness the light traveling at 0.134c relative to the spaceship one direction, and 1.866c relative to the spaceship the other direction. Where I was stuck was when I was for some reason thinking that it didn’t have to come back to the space ship. You probably could guess this, but I feel pretty stupid right now!

Also, just to make sure that I had a grasp on the subject, I ran the same calculations that you made, only in the assumption that the laser was fired from the front of the space ship. It worked out exactly the same, just like it should.

Thanks a bunch for all the help, guys! I know how frustrating it can be when you try to explain something in the best way you know how, and the guy you are explaining it too just doesn’t get it. Thanks for having patience with me.

 

[The New Guy]

Oh yeah, one more quick question about relativity, but this one shouldn’t prove frustrating. Suppose that Planet Neptune considers itself to be perfectly round. Also suppose that we here on Earth are capable of observing Neptune from a telescope, and also capable of making precise measurements of Neptune’s diameter from here on Earth. Now, let’s say that we got into an orbital pattern such that Neptune was moving relative to us in a crossways direction. In that case, we would actually measure Neptune to be slightly oval shaped due to length contraction, right?

 

[ghwellsjr]

Oh yeah, one more quick question about relativity, but this one shouldn’t prove frustrating. Suppose that Planet Neptune considers itself to be perfectly round. Also suppose that we here on Earth are capable of observing Neptune from a telescope, and also capable of making precise measurements of Neptune’s diameter from here on Earth. Now, let’s say that we got into an orbital pattern such that Neptune was moving relative to us in a crossways direction. In that case, we would actually measure Neptune to be slightly oval shaped due to length contraction, right?

When viewed through a telescope a spherical body, even when traveling at a very high speed will appear to be perfectly round. However, with proper measurements, it would be determined to be oval shaped. See:

http://en.wikipedia.org/wiki/The_Terrell-Penrose_Effect

 

[The New Guy]

Wow! That is facinating. I never would have thought of it. I actually googled the Terrell-Penrose Effect, and found this site <http://th.physik.uni-frankfurt.de/~scherer/qmd/mpegs/lampa_terrell_penrose_info.html> It really helped me to visualize what was going on here. Thanks for the help!

 

[Naty1]

Newguy: You should take a look at Einstein's original RELATIVITY...The book is available for free online and Einstein explains special relativity using high school algebra...

Also you should recognize

I have most of the concepts at least “memorized.” I don’t necessarily “understand,”...

is an issue (for everyone) because relativity (and quantum mechanics, and a number of other areas of physics) requires new rules, new ways of thinking, new LOGIC, and our everyday day experience does NOT reveal those to us. For example, while you cannot expect the clock of a rapidly moving friend to agree with your stationary clock...who would have expected that from our everyday experience?? It took an "Einstein"!

For example black holes are NOT logical in everyday thinking...but even Einstein refused to believe they could exist. Is quantum mechanics "logical" : again, even Einstein refused to believe the imprecision, the statistical limitations, it imposes.

 

[harrylin]

Newguy: You should take a look at Einstein's original RELATIVITY...The book is available for free online and Einstein explains special relativity using high school algebra...

Yes. http://www.bartleby.com/173/
But see also:
http://www.fourmilab.ch/etexts/einstein/specrel/www/
That earlier and more precise formulation about SR is sometimes clearer.

[..] relativity (and quantum mechanics, and a number of other areas of physics) requires new rules, new ways of thinking, new LOGIC, and our everyday day experience does NOT reveal those to us.

I disagree! Although our everyday day experience is different, every time that people told me (and almost convinced me!) that I should use "new logic", it turned out that some subtle aspect was not well understood. There are no other "logics": either our thinking is logical and correct in principle, or illogical and therefore in principle wrong. In particular SR does not require a new way of thinking (indeed, much to my surprise).

For example, while you cannot expect the clock of a rapidly moving friend to agree with your stationary clock...who would have expected that from our everyday experience?? It took an "Einstein"!

Not really
Larmor, Lorentz-Poicare, Einstein ...
- http://en.wikipedia.org/wiki/History_of_special_relativity

For example black holes are NOT logical in everyday thinking...but even Einstein refused to believe they could exist. Is quantum mechanics "logical" : again, even Einstein refused to believe the imprecision, the statistical limitations, it imposes.

Unexpected is different from illogical. And the biggest remaining issue is, IMHO, not free will vs. predestination, but Bell's theorem (and it's still not solved!).

Cheers,
Harald

 

[The New Guy]

Thanks for the input, guys! I will not argue whether relativity and QM require new logic or not. I will, however, say that it is much harder to learn about relativity and QM because the effects are nothing like we experience in everyday life; although, with the right equipment you can observe wave-particle duality in QM. As far as relativity goes, it sure would be great if I could jump into a spaceship and accelerate to 0.9c so that I could actually observe the effects. Everybody learns better by actually observing things. Some of the physics that we observe in everyday life is totally second nature to us, but yet, if it was not observable it would be very difficult to in vision. For example, if you set a hammer down on a slanted rooftop, it might stay right there, but yet, if you give it any little push to start it moving, it will never stop until it hits the ground. I can’t imagine trying to explain that to somebody who has never seen it and doesn’t understand it. However, that is kind of the mission when it comes to learning about relativity and QM.

I will have to take a look at that book. Special Relativity in terms of algebra is something that I could understand. I am a college student right now, and will be taking calculus this semester, but for now, I know no calculus. Most of the equations that you run into in relativity don’t require anything special beyond algebra to manipulate, but that is only if you are plugging numbers into them and solving. If you actually want to understand where most of the equations were derived from, you need to know calculus. I'm anxious to see how Einstein explains it in terms of algebra.

 

[cryticfarm]

I have read through the thread, and I am still having trouble understanding how it is possible for a physical object to age slower near the speed of light than it's still counterpart, even after it has slowed down and observed from any frame of reference. I understand the light clock, but how would that principle apply to for example, a watch, that doesn't use light pulses to calculate time.

 

[CDCraig123]

In really simple terms the faster you move through space-time that faster time passes for you. The real question is what if you could stop moving have zero speed what would time do.

 

[WannabeNewton]

In really simple terms the faster you move through space-time that faster time passes for you.

Not quite correct. In your reference frame time never passes "faster" or "slower" for you. Remember that in your reference frame you are at rest so the components of your 4- velocity are zero except for the one corresponding to the time basis. However, other objects that are not at rest relative to you will experience a time dilation as measured in your frame.

 

[GrayGhost]

I have read through the thread, and I am still having trouble understanding how it is possible for a physical object to age slower near the speed of light than it's still counterpart, even after it has slowed down and observed from any frame of reference. I understand the light clock, but how would that principle apply to for example, a watch, that doesn't use light pulses to calculate time.

Well, it's all the same no matter what the nature of the time piece used. So wrist watch vs lightclock vs planetary motion vs atomic clock, doesn't matter. Everything is governed by the rate at which time itself goes by. Just as the photon bounces slower per the moving observer, so too do the arms of a mechanical clock attached to the lightclock revolve slower. As someone here already mentioned, you can replace the bouncing photon with a steadily bouncing ball. The result is the very same. A steady bounce is just to say "a steady cyclic activity" of any kind. No matter what the activity, if it's of material nature, then it ages because time goes by. The ticking of a time-piece is the aging of a time-piece.

There's much more to it than that, but to go into that opens up many more cans of worms that you are likely not ready for yet. Technically, the rate at which time passes by me per me is the same rate at which time passes by you per you. That's called "the rate of proper time". Wrt the interval between 2 defined events, the LTs relate a duration of a moving clock (per you) to the duration of your own clock (per you), which yields a "relative rate of time" in which the moving clock always runs slower. It's a frame-to-frame relation.

GrayGhost

 

[CDCraig123]

You are right Newton but if you put a man on a spaceship and his speed was 99% of the speed of light for 5 years when he gets off his ship a lot more then 5 years will have passed when compared to someone on Earth as we are only traveling 0.1933% of the speed of light. So it would seem that faster you move through space-time the faster time travels for you, but only when you have a reference point to compare it to that is moving slower.

 

[Drakkith]

I have read through the thread, and I am still having trouble understanding how it is possible for a physical object to age slower near the speed of light than it's still counterpart, even after it has slowed down and observed from any frame of reference. I understand the light clock, but how would that principle apply to for example, a watch, that doesn't use light pulses to calculate time.

The light clock is simply an example of how time dilation works. Time slows down at high speeds relative to another frame because nothing can travel faster than c in any frame, not even light. A light clock is very very useful because light is the only thing that does travel exactly at c. If we simply did the experiment with matter then one could easily ask why time dilation happens as the matter isn't traveling faster than c yet and there should be no reason for time dilation to occur. The EFFECT of time dilation is identical for everything. It doesn't work different between light pulses and matter.

A better way of understanding it is to look at everything and realize we are traveling in SPACETIME, not just space. I'll try to explain it, but I won't gurantee 100% accuracy here. An object at a standstill in space travels at c through spacetime. As it's speed relative to another object increases, it travels faster in the space dimensions and slower in the time dimension to keep the overall speed through spacetime at c. It isn't as easy as adding the space speed with time speed, but instead follows the equation for time dilation.

 

[The New Guy]

cryticfarm,

I would go out on a limb and say that I am in nearly the same boat as you. What has helped me the most in understanding what I do about special relativity are examples of why it simply has to be. I do not guarantee that the information I am about to give you is 100% accurate, but I will try to explain what I have learned to you in the way that was most helpful to me.

Fact: The speed of light (in a vacuum) will be observed at exactly speed ‘c’ from ALL frames of reference, even if they are in relative motion. For example, if a pitcher that could throw a 100 mph fast ball was standing on the ground and threw the ball at me, I would measure its speed at 100 mph. However, if that same pitcher was standing on a truck that was traveling straight towards me at 50 mph, and threw the same ball, I would measure the ball’s speed at 150 mph. Likewise, if the truck was traveling away from me, I would measure the speed of the ball at 50 mph. This is an example of classical relativity at its finest.

Now, let’s replace the ball with a flashlight. How is this different? Well, if that pitcher was standing on the ground and shined the light at you, you would measure the speed of the light at speed c. No problem here, but however, when the pitcher shines that light at you from the truck moving towards you, you will not measure the speed of the light at c + 50 mph, you will measure it at c. Likewise, if the truck is moving away, you will not measure the light at c - 50 mph, it will be exactly c. (This is assuming you are in a vacuum.)

Now, we have a real problem here! You see the light at c, and he sees the light at c, but yet, you are in relative motion. How is this possible? Einstein came to the rescue. He postulated that if everyone is to agree on the speed of light, they must disagree on the measures of space and time. This comes in three forms – time dilation, length contraction, and relative simultaneity.

Do you understand the idea of length contraction, and why this has to be? I’m not quite sure if I do, but I will try to explain what I have heard about length contraction. This is really testing my knowledge, so don’t quote me on any of this because I will likely screw up.

Suppose we go back to the spaceship scenario. We will have one observer floating in random space, and a spaceship with a 10 light second ruler hanging off the front, and another off the back. Only this time, instead of putting mirrors on the ends of the rulers, let’s put lightning rods there. The spaceship flies past the observer at near the speed of light, and just as the spaceship is flying past, the observer sees two simultaneous lightning strikes, one on each lightning rod. Meanwhile, the spaceship flies into the light from the strike in front of him, and the light from the strike in back of him has to chase him down from behind. He sees the strike in front first, and the one behind a while later. From the space ship’s frame of reference, both lightning strikes travel the exact same distance (10 light seconds), at the exact same speed, speed c. Distance=Rate X Time, so that means that both lightning strikes took the exact same amount of time to reach him. The fact that he saw the one in front of him first means that the one in front of him actually happened first.

Now, getting into length contraction (This is where I really get shaky, so don’t take my word for this.), the observer sees the two lightning strikes at the ends of the space ship’s rulers as being simultaneous. However, from the space ship’s frame of reference, the front lightning strikes first, and the back lightning strikes a little while later. In the time between strikes, the space ship, both rulers, and both lightning rods advance ahead. The lightning rod in the back advances closer to where the lightning rod in the front was when the front lightning struck. This would mean that the physical space between the two lightning strikes was actually shorter. In order for the spaceship and the observer to agree on where the two lightning strikes occurred, the space ship, both of his rulers, and both lightning rods would have to be seen by the observer as contracted in the direction of motion. As I said, don’t take my word for any of this. If any of this is wrong, I hope somebody else will point it out.

I’m hoping that now you have a understanding of why relative simultaneity, and length contraction have to be, and with that, you will be able to understand why time dilation must affect more than just light clocks. This takes us right back to what ghwellsjr started out by saying:

If you agree that the ruler that the traveler is carrying with him is length contracted along the direction of motion, then when he measures the speed of light using that ruler to measure the distance the light travels during some period of time, he will get the wrong answer unless his clock is also ticking at a slower rate.

From here, I would like to refer you to another post by ghwellsjr. This one helped me a lot in understanding time dilation:

You need all three: time dilation, length contraction and relativity of simultaneity. Let me work our your problem in a way that may make it obvious to you.

You stated you have a ruler 10 light seconds long so that when the laser fires, it will take 10seconds for the light to get to the end. However, you cannot see that happening. What you need to do is put a mirror at the end of your ruler so that the light can be reflected back to you and then you will measure 20 seconds elapsing on your watch, confirming that the light did indeed travel the 20 light seconds in 20 seconds.

Now the guy on the spaceship has a similar mirror on the end of his ruler which you say is scunched down to 5 light seconds. You can work the Lorentz factor equation backwards to determine that he is traveling at 86.6%c, correct?

Now if he is traveling at 86.6%c to the right, his mirror is also traveling at that same speed, correct? So now it won't be too hard to figure out how long it will take for the laser beam traveling to the left at c to meet the mirror traveling to the right at 0.866c. It's a simple ratio and it turns out to be 2.68 seconds. Can you figure that out? This also means that the mirror and the spaceship have traveled 2.32 light seconds to the right.

Next we notice that the laser beam is changing direction and the difference in speed between the laser beam and the mirror tells the relative speed between them and that is 0.134c, correct? Now at this speed, the laser beam has to travel 5 light seconds to get to the other end of the ruler and that will take 37.31 seconds, correct? And that is when the guy on the spaceship sees the return laser flash just like you did on the ground. The total elapsed time for him, according to ground time, is 39.99 seconds, but according to him, since his clock is running at half speed is just about 20 seconds, the same as you measured. (The slight error is caused by rounding off the numbers.)

Remember, he thinks his ruler is 10 light-seconds long, so his measurement of the speed of light is the same as yours.

I think you can see the parts that length contraction and time dilation play in this analysis. Simultaneity has to do with the fact that for you, the two halves of the round trip for the laser beam took the same time but as far as you are concerned they were way different for the spaceship guy. If we had done the analysis from his point of view, he would say that the two halves were equal for his ruler and mirror but yours were the ones that were way different.

One last thing: we can calculate how much farther the spaceship had to travel before the reflected laser beam was detected and that is 32.31 light seconds for a total of 34.62 light seconds which is the distance the spaceship traveled in 40 seconds (according to you) at 86.6%c (ignoring round off errrors).

I'm not sure where you got the 25 seconds or why you thought time must be progressing faster for him but hopefully this explanation will clear everything up for you.

 

[harrylin]

[..]
Do you understand the idea of length contraction, and why this has to be? I’m not quite sure if I do, but I will try to explain what I have heard about length contraction. This is really testing my knowledge, so don’t quote me on any of this because I will likely screw up.
[..] Now, getting into length contraction [..]

I did not follow your explanation, so perhaps it was correct.
It may be useful to know how the length contraction assumption started; it has nothing to do with relativity of simultaneity and it's less complex without it.
Just check out the Michelson-Morley interferometer, it works with two return paths in different directions and it was expected (ignoring length contraction!) to enable a detection of absolute motion, in particular the simple calculation on p.336:

http://en.wikipedia.org/wiki/File:Michelson-Morley_experiment_(en).svg

See also a clearer picture here:
http://en.wikipedia.org/wiki/File:Michelson-Morley_experiment_(en).svg

Later a similar experiment was done (with different arm lengths) that should have given a detection of absolute motion in case of length contraction without time dilation, see:
http://en.wikipedia.org/wiki/Kennedy–Thorndike_experimentHarald

 

[The New Guy]

As I said, my understanding is less than sufficient, so if you say my description of the Lorentz Contraction does not make sense, it probably doesn’t.

What has helped me the most in trying to understand this stuff is a description that starts with a constant speed of ‘c’ that must preserved in all reference frames, and from there goes down the list of length contraction, relative simultaneity, and time dilation, and explains why each is needed if the speed of light is to be preserved for objects in relative motion. That’s what I was trying to do here.

I understand that the relativity of simultaneity is somewhat different than the other two. It is something that I’m sure even classical physics could have predicted under an assumption that light is no different than anything else, for example, sound. The difference is that classical physics would have predicted that two simultaneous events could be perceived to happen at different times by other observers, but actually happen at the same time; whereas in relativistic physics, two events that happen simultaneously for one observer actually happen at different times for other observers. They are not only perceived to happen at different times. It seems to me that, since the speed of light is not relative, the relativity of simultaneous events would have to be very intimately tied to time dilation and length contraction. In other words, it seems like there would have to be a means of explaining the relativity of simultaneous events through length contraction, and time dilation. Whether my thought process was correct is a big “?,” however.

 

[BruceW]

That sounds pretty much correct to me. This is the way I'd explain it: inertial reference frames transform under the Lorentz transformations because the speed of light is unchanged whenever you apply a Lorentz transform.
And time dilation, length contraction, relative simultaneity are all specific consequences of the Lorentz transform.

 

[harrylin]

[...]
What has helped me the most in trying to understand this stuff is a description that starts with a constant speed of ‘c’ that must preserved in all reference frames, and from there goes down the list of length contraction, relative simultaneity, and time dilation, and explains why each is needed if the speed of light is to be preserved for objects in relative motion. That’s what I was trying to do here. [..]

Calculation-wise yes; however, see further.

I understand that the relativity of simultaneity is somewhat different than the other two. It is something that I’m sure even classical physics could have predicted under an assumption that light is no different than anything else, for example, sound. The difference is that classical physics would have predicted that two simultaneous events could be perceived to happen at different times by other observers, but actually happen at the same time; whereas in relativistic physics, two events that happen simultaneously for one observer actually happen at different times for other observers. They are not only perceived to happen at different times. [..]

Except for the first sentence, that's a definite no. "Speed of light", like any other physical term, has an operational definition in SR - it says nothing about "actual". Quite to the contrary: it says that different observers have a different perception of reality, and nobody can measure who is right. The difference of simultaneity with the other two effects is that it is directly made by the observer, if following the definition of SR.
In a nut-shell: nature makes the two-way speed of light c, and men make the one-way speed of light equal to the two-way speed of light. For more on this, see my post #18 here:
https://www.physicsforums.com/showthread.php?t=518005&page=2

It seems to me that, since the speed of light is not relative, the relativity of simultaneous events would have to be very intimately tied to time dilation and length contraction. In other words, it seems like there would have to be a means of explaining the relativity of simultaneous events through length contraction, and time dilation. Whether my thought process was correct is a big “?,” however.

If you studied the subject matter of my last post (but apparently you did not), then you saw that time dilation and length contraction are fully independent of our choice of distant simultaneity. However, with that choice we make the one-way speed of light equal to the two-way speed of light, and also the measurements of time dilation with distant clocks become consistent. In that way the effects are all related.Harald

 

[The New Guy]

Harald,

Thank you for your concern in my trying to understand SR. However, I regret to say that I had a little difficulty following your prior post.

You started out by quoting me, and replying with, “Calculation-wise yes; however, see further.” I’m not sure what you meant by that. The statement of mine that you quoted was not a question.

Secondly, I understand that there is no “actual” in SR. As far as simultaneous events go, one person sees them as simultaneous, the next sees one before the other, and the next sees the other before the one. None of them can say that the events “actually” happened at certain times because what each person sees is correct. There simply are no “actuals.” Am I correct up until this point? Also, it is in classical physics where “actual” can become a valid statement, right? In classical physics, two lightning strikes could be truly and actually simultaneous even if different observers see them at different times due to relative motion. This is what I was trying to say when I was explaining that classical physics could have predicted relative simultaneity. It could have predicted that it would be possible for different observers disagree on the time that two events happened, but in classical physics, they would both be wrong because the events “actually” happened at a certain time/times. However, by preserving the speed of light, SR takes the “actual” out of relative simultaneity, right? I know I did not explain that well, but that is the best I can do. If you do not follow me, I don’t blame you.

Next, you lost me with the talk about the one-way speed of light versus the two-way speed of light. I looked at the thread that you referred me to, and read your reply. However, it was over my head.

Lastly, I did take a look at the links you referred me too of the Michelson-Morley Interferometer, and the Kennedy-Thorndike Experiment. However, I did not find any p. 336. All I saw was a picture of the Michelson-Morley Apparatus and a short write-up on the K-T Experiment. Sorry about that. I should have explained it in my reply.

 

[GrayGhost]

Secondly, I understand that there is no “actual” in SR. As far as simultaneous events go, one person sees them as simultaneous, the next sees one before the other, and the next sees the other before the one. None of them can say that the events “actually” happened at certain times because what each person sees is correct. There simply are no “actuals.” Am I correct up until this point? Also, it is in classical physics where “actual” can become a valid statement, right?

Hello The New Guy.

Technically per SR, no observer is more wrong than the next even given their disagreement. Equivalently, each are equally correct, even though they disagree. Bottom line, per the LTs they agree they should disagree and they agree on their disagreements. Just as in classcial mechanics, there is no violation, because each uses the same laws of mechanics and each takes measurements that match their predictions. Remember that at non-luminal velocities, SR reduces to classical mechanics. Classical mechanics never addressed the bizarre affects that must arise given luminal motion. So SR is really but an extension of classical mechanics. You know, had Newton not been so busy creating physics and calculus from thin air, I would not be surprised had he created special relativity on his own in the late 1600s or early 1700s, had he "known" light's speed was invariant. However, it's likely he'd have developed it from the foundation of an aether as Lorentz did, instead of Einstein's version which was indifferent to any existing aether.

GrayGhost

 

[harrylin]

Harald,

Thank you for your concern in my trying to understand SR. However, I regret to say that I had a little difficulty following your prior post.

You started out by quoting me, and replying with, “Calculation-wise yes; however, see further.” I’m not sure what you meant by that. The statement of mine that you quoted was not a question.

Your statement could suggest that nature imposes a one-way speed of c on our measurements; however Einstein stressed that instead, this is our doing (and SR does not depend on what an observer does or doesn't do!).

Secondly, I understand that there is no “actual” in SR. As far as simultaneous events go, one person sees them as simultaneous, the next sees one before the other, and the next sees the other before the one. None of them can say that the events “actually” happened at certain times because what each person sees is correct. There simply are no “actuals.” Am I correct up until this point?

Not really: multiple contradictory statements cannot be all correct. See GrayGhost's clarification.

Also, it is in classical physics where “actual” can become a valid statement, right?

In both, "actual" can become a valid statement and in both there are "appearances". Only SR has much more of such "relative" statements than classical physics.

In classical physics, two lightning strikes could be truly and actually simultaneous even if different observers see them at different times due to relative motion. This is what I was trying to say when I was explaining that classical physics could have predicted relative simultaneity.

Talking of "actually" : classical physics actually had relative simultaneity.
see http://en.wikipedia.org/wiki/Relativity_of_simultaneity#History

It could have predicted that it would be possible for different observers disagree on the time that two events happened, but in classical physics, they would both be wrong because the events “actually” happened at a certain time/times. However, by preserving the speed of light, SR takes the “actual” out of relative simultaneity, right?

SR doesn't pretend anything about "actual"; its definitions are operational, just like QM.

I know I did not explain that well, but that is the best I can do. If you do not follow me, I don’t blame you.

I followed you - and it's almost right.

Next, you lost me with the talk about the one-way speed of light versus the two-way speed of light. I looked at the thread that you referred me to, and read your reply. However, it was over my head.

What matters is that two-way measurements (such as with Michelson-Morley) cannot care less about relativity of simultaneity; therefore also length contraction and time dilation do not depend on it.

Lastly, I did take a look at the links you referred me too of the Michelson-Morley Interferometer, and the Kennedy-Thorndike Experiment. However, I did not find any p. 336. All I saw was a picture of the Michelson-Morley Apparatus and a short write-up on the K-T Experiment. Sorry about that. I should have explained it in my reply.

Sorry indeed a copy-paste went wrong!
Here's the link:
http://en.wikisource.org/wiki/On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_EtherHarald

 

[BruceW]

Secondly, I understand that there is no “actual” in SR. As far as simultaneous events go, one person sees them as simultaneous, the next sees one before the other, and the next sees the other before the one. None of them can say that the events “actually” happened at certain times because what each person sees is correct. There simply are no “actuals.” Am I correct up until this point? Also, it is in classical physics where “actual” can become a valid statement, right? In classical physics, two lightning strikes could be truly and actually simultaneous even if different observers see them at different times due to relative motion. This is what I was trying to say when I was explaining that classical physics could have predicted relative simultaneity. It could have predicted that it would be possible for different observers disagree on the time that two events happened, but in classical physics, they would both be wrong because the events “actually” happened at a certain time/times. However, by preserving the speed of light, SR takes the “actual” out of relative simultaneity, right? I know I did not explain that well, but that is the best I can do. If you do not follow me, I don’t blame you.

Yeah, the only 'actual' in relativity is when world lines meet. For example, when two people high-five, then as viewed by any observer, the two people's hands will meet at the same time and same place.