# Speed of the light and dilation of time

1. May 10, 2012

### uniqueland

If I am 35 years old and I am in a train sitting in a special tube that is built around the entire circumference of the planet. Putting aside all of the questions of practibility and g forces and the like, if the train I am in accelerates to just a hair under the speed of light and I travel on this train until my 5 year old son is 35 years old, at which time my train wil come to a complete stop and I will disembark my "light speed" train and meet my son at the "train station" when I walk out, will we both be the same age?

Follow up question is, whatever the number of revolutions around earth that my light speed train would make per day multiplied by 365 days multiplied by 30 earth years, would my light speed train in fact make that many revolutions or would it make less. To me, riding on the train, almost no time at all would have passed, but to my son, waiting for me outside the tube where my train is traveling at near light speed, 30 years would have passed. If there was a digital display outside the tube counting the revolutions one by one and adding to the total another "1" each time my train passed the starting point, at the end of 30 years I would have some very large number of revolutions. BUT if I, while riding this train, were wearing a watch AND this watch ALSO counted revolutions, would the amount of revolutions show the same as the counter outside the train counted AND would the time on my watch show that 30 years have passed or something much less?

Last edited: May 10, 2012
2. May 10, 2012

### Staff: Mentor

Re: Speed of the light and time dilation

Yep - search this forum or google "twin paradox" for more details.

You both will agree about the total number of revolutions. You will disagree about how much time passed during each revolution - you will experience less time, so will age less, during each revolution than your son. And your watch will also be behind that of your son.

3. May 11, 2012

### yuiop

Re: Near Light Speed Travel & Time Dilation... I don't get it.

Technically the answer is no. If you were exactly 35 years old when you got on the train then you will be older when you get off the train, for example you might be 35 years and one day old. For no time at all to pass for you on the train you would have to travel at exactly the speed of light which is physically impossible. If you waited until your son was 36 years old it would be possible to go at a certain speed such that you are also exactly 36 years old when you reunited.
Yes.
Your watch would show something much less (eg one day) and you will have physically aged much less than 30 years. If you stayed on the train long enough, your son could end up physically much older than you.

4. May 11, 2012

### HallsofIvy

Staff Emeritus
Any integer result, such as the number of times you have gone around the earth is invariant. Both you and son would calculate the circumference of the earth, in your respective frames of reference, he dividing by your speed relative to the earth, you dividing by the speed of the earth relative to you, to find the number of rotations you have made. But, comparing your calculations, you would have used the contracted distance (relative to his distance) and the dilated time (compared to his time). Since the same Lorenz contraction factor is used in both distance and time, that will cancel giving you both the same result.

5. May 11, 2012

### Mentz114

Strictly speaking, the difference in age can be attributed to the fact that the proper time along the two worldlines between boarding and alighting, is different. Not 'time dilation', but differential ageing.

6. May 13, 2012

### sunjin09

Since I just started reading SR, I only want to make a comment. Since the lightspeed train is accelerating by going around the earth which is assumed to be an inertial frame, the train is certainly not an inertial frame, therefore the time dilation should be modified in such a system. Is it possible that the modification due to acceleration brings everything back to normal so that you are still 30 years older than your son?

7. May 13, 2012

### HallsofIvy

Staff Emeritus
While there are complications involved in the fact that the train is not moving in a straight line, they are NOT sufficient to completely overcome the affects of the highspeed motion.

8. Jun 1, 2012

### uniqueland

T 08:28 AM
uniqueland
This Message is Moderated

If I am on this train traveling at 99.99% light speed around the circumference of the earth for 30 earth years. My watch, which is synchronized to count each revolution my train makes around the earth, will show those revolutions blurring by at a much faster rate than the earth based revolution counter display outside the train station because it will count 30 years worth of revolutions in just say one day to me. When I get off the train, my watch will match the number of revolutions shown on the revolution counter outside the train station but the time on my watch might say that only a day has passed when 30 years have passed outside my train. If I was skyping with my wife, my "viewing" would be one big blur, because I would be seeing her over 30 years but speeded up to all be shown in one day to me and she would see me as practically a frozen image because I would be going by in only one day to her 30 years. It might take a year for her to see my mouth move. Correct?

9. Jun 1, 2012

### ghwellsjr

At 99.99% light speed, you would age about 5 months in 30 years of earth time. For you to age only 1 day, you would have to go more than 99.99999999% light speed. But otherwise, your conclusions are correct.

10. Jun 4, 2012

### uniqueland

Re: Speed of the light and time dilation

So, let's take this to the next level. Are you saying that, for example, I will feel like I just got on the train a few hours ago, or maybe a day ago, and maybe I will watch a couple of two hour movies on my ipad, which will take 2 of my hours each to watch but when my train comes to a stop, 30 years will have passed on earth. So, to my son, who might ask me what I have been doing for the past 30 years, I would answer that I watched a couple of 2 hour movies on my ipad. but to him, it would seem like in 30 years the only thing I accomplished was that I watched two movies, took one shower and had one meal, but to me I was only on that train for 4 hours and did not have time to really do much else, whereas my son would have accomplished 30 years worth of experiences in that same time . Correct? If my son was watching a monitor of an onboard video camera focused on me on this train, I would be moving in such slow motion I would appear practically frozen to him. Is that right? And if that is the case, then my revolution counter I had on board the train with me would be whizzing by at a far greater rate than 6 or 7 revolutions per second, even though, at just under the speed of light, that would be the maximum revolutions per second the light speed limit will allow me to have. So if my train is physically passing go on each earth revolution, how can my revolution counter onboard the train show that I had 30 earth year's worth of revolutions when my watch says I have only been on this train for a few hours, and, in those few hours, in order to have that many revolutions travelling that distance around the circumference of the earth at just under light speed, I would have to be traveling at thousands of times more than light speed, so how is this explained? Additionally, if you continue that thought, I could travel to the end of the universe, 13.7 Billion light years away and back again, traveling at the smallest fraction just under the speed of light and the entire 27 billion earth year journey would only feel like maybe a day to me and when I returned to earth, I would be a day older but the earth, sun and entire solar system would most likely be gone by that time, and maybe even the milky way and the entire universe too. Right? And if that is the case, then, if we could achieve just under light speed, we could travel to the end of the universe (putting aside of course that there would be a hundred other reasons why this could never be practical) but the problem is we here on earth would never get to hear anything of our journey because we would not return for almost 30 billion years even thought the space travelers would only be a day older than the day they left earth. Is all of that correct?And if this is correct, then, if we could achieve near light speed just under by the smallest fraction, we could theoretically all migrate from the earth (if we absolutely had to one day) to some far off galaxy maybe thousands of light years away, and get there in the lifetimes of the original travelers because, while the earth we left behind may be thousands or millions of years older, we would have aged a few days, months or years, depending on how close the the speed of light we were traveling. Is all of that correct?

Last edited: Jun 4, 2012
11. Jun 4, 2012

### Staff: Mentor

Re: Speed of the light and time dilation

Yes.

I know that it sounds utterly absurd. It's worth noting that
- These extraordinary phenomena only happen under extraordinary conditions. For example, we could detonate all the nuclear weapons on earth at once, and the energy released would be as the belch of a gnat compared with the energy required to send you on your 37-billion year journey. The way we see the world working day-to-day doesn't tell us much about what to expect under those conditions.
- The equations that predict these extraordinary phenomena also all predict normal day-to-day behavior at normal day-to-day speeds.
- Where we have been able to measure the effects (very small objects such as subatomic particles, moving at very close to the speed of light; much larger objects such as satellites moving at a few miles a second, still a mere crawl compared with the speed of light) the measurements match the predictions.

12. Jun 6, 2012

### uniqueland

Thanks for your reply. But I still do not understand the paradox of how can my onboard counter, count 30 years worth of revolutions around the earth when, to me onboard the light speed train, I will feel that I have only been on this train for a few hours, and, if I multiply the number of revolutions I would make per second going at just under 186,000 mps by the number of seconds my onboard watch counted for the few hours it said I was on this train (even though 30 earth years passed outside the train). In order to mark 30 years worth of completed revolutions I made around the planet in the few hours I was on the train, I would have had to have been going thousands of times the speed of light to accomplish that many revolutions in only a few hours. Is there any sensible explanation to this or is just a paradox with no explanation?I guess it is the same paradox that, if I wanted to travel 27 billion light years in only a day, I would be have to have been traveling at an exponentially high muliple of the speed of light to cross that much distance in only a day. Is the answer that, it wasn't only a day. It was in fact 27 billion years that it took to make the journey to the end of the universe and back. It is just that, for me, time virtually stopped I would have lived those 27 billion years as if I was living for one day. Yet, if I could look out the window and see the galaxies and outside would I be viewing 27billion light years worth of "scenary" whizzing by as if I was making the entire journey in only a day, whereas to someone watching my journey from earth though an immensely powerful telescopo for tracking my journey, would be watching me make my journey over a period of 27 billion years (putting aside of course the issues of lifespans and making hte assumption, for p;ruposes of this example, that the observer watching me through a telescope would be immortal and woudl still be alive 27 billion years from the time I departed.So, for purposes of my example, assuming everything in the universe stopped moving and remained frozen light an immense painting, and I was traveling though this static universe until i got to the end 13.7 B light years away and back again, at near light speed, I would see the stars, galaxies and other phenomenon whizzing by my window, but, because I would be making this 37 billion year journey in only a day, because time for me would have virtually all but stopped, would I be viewing the objects I was whizzing by as if I was traveling at many times light speed because so much more of the outside would pass by my windown with each passing second of my impossibly long "seconds" because each light century to me would seem only a light second.So then if we could theoretically make the journey to Mars (maybe by teleportation) at just under light speed with no concern for g forces or other such problems of impractibility, technically, I would get to Mars instantly, but on earth, they would be waiting maybe 20 minutes or so for me to emerge from my telepod on Mars. So I would get in my light speed telepod on earth and emerge on the one on Mars, having traveled at just under light speed, but when I contacted earth and told them I was safe and I made it to Mars, over 20 minutes will have passed on earth even though my watch would show that I arrived on Mars the instant I stepped into the telepod on earth and that only a second or so would have passed, and it would take them another 20 minutes to get the message that I had arrived safely. Correct?

Last edited: Jun 6, 2012
13. Jun 6, 2012

### ghwellsjr

You are correct in most everything you said in post #10 and #12 but you are overlooking the fact of length contraction so as far as you are concerned when you travel to the remotest parts of the universe, you aren't going very far, they are very close to you and they are contracted along the direction of motion.

Also, when you point out that after returning, the earth may not be here any more, you have to note that the distant locations that you are traveling to may not be there when you get there. You will be watching those locations age in high speed as you approach them.

Now as to your questions about circling the earth at high speed, you would also see the earth length contracted and being distorted in such a way that you would conclude that your distance around the earth was very short. You would never measure yourself to be traveling greater than the speed of light.

Now about your trip to Mars: when the earthlings are watching you travel at just under the speed of light, they will see you traveling at just under one-half the speed of light because they have to wait for the images of you to get back to them. So it will take them 40 minutes to see you get to Mars and at that time, they will see you report back your safe arrival.

14. Jun 7, 2012

### uniqueland

thanks George. I hadn't considered that my destination to the end of the universe would be 13.7 billion years older by the time I got there too and may not be there anymore, just like the earth and milky way might be when I returned 27 billion earth years later. But what about my window question? Assuming that my eyes could actually focus and take in that much viewing at that insanely high speed and assuming that for the purposes of my example, the entire universe froze in place and stopped moving so that I would be traeling through a universe that was an immense static canvas, would I be able to view 13.7Billion light years worth of scenary all in one of my spaceship days. For example, if there were 100 trillion galaxies that I would pass by on my way the the most distant galaxy I had identified as my destination point before I left that was 13.7billion light years away, would I actually see all 100 trillion galaxies whizzing past my window as I made my 13.7billoin light year journey (which would seem like only one day to me, and even though to an observer on earth, it would take me 13.7 billion years to view all that scenary.

As for my telepod to Mars, I am assuming that my teleportation woudl be at .99999999% the speed of light so I would emerge on Mars in say around 20 minutes (I haven't calculated how many light minutes away is Mars but I think it is around 20) but my watch would show only maybe that one second had passed from the time I got into the earth telepod to the time I emerged from the Mars telepod. And then, if I turned right around and got right back into my telepod after spending only a few seconds on Mars, 40 minutes would have passed on earth from the time I first entered the earth telepod to the time I came back from Mars and disembarked from the earth telepod, but to me, it would have seemed like I made the entier round trip journey in only a few seconds. Is that correct?

Also, in my light speed earth train, same question. If I was looking out the window, and assuming my human eyes could actually deciphor images at such insanely high speeds, would I see the train station pass my window on each of my 30 earth years worth of revolutions at the speed of light, which would be some crazy high number, even though my watch would show that I only spent maybe an hour or so in that train, in which case, the number of times I would see that trains station should be equal toonly the number of revolutions I would have made in my light speed train traveling for only those few hours which would be far lesll than it would traveling for 30 years of course. If X is the number of revolutions I would make traveling at just under light speed for a few hours and Y is the number of revolutions i would make in my earth light speed train if I were traveling for 30 years (to an observer at the train station), looking out the window my entire journey, how many times would I see the train station pass before my eyes during my 4 light train hour (and 30 earth year)ride, X or Y?

Last edited: Jun 7, 2012
15. Jun 7, 2012

### ghwellsjr

The images that you would see with your naked eyes would be extremely distorted because everything in front of you would be blue shifted out of your visible range and everything behind you would be red shifted out of your visible range and most of those 100 trillion galaxies would be off to your side which means the light from them would be color shifted to varying degrees depending on their angle to you which of course will be changing rapidly. The different color shifting also goes hand in hand with the view of aging so, in the forward direction, you would see 27 (not 13.7) billion years of aging happen in a day while behind you our Milky Way galaxy and others would appear to have aged just a day. And other galaxies in between would have differing amounts of aging. Let's assume that you either have magic eyes or video equipment that can color shift the images back into the visible range.

Not only that, but it would take 27 billion years for the earthlings to watch you arrive at your distant location (of course your image will also be red shifted out of their visible range so we'll give them the necessary video equipment) and they will see that you have aged only a day when you got there.

Now on your return trip, everything will be reversed. That's when you will see the Milky Way galaxy go through 27 billion years of aging while the galaxies you left behind won't age hardly at all and the ones off to the side have differing aging. When you get back to earth, everything will have aged 27 billion years, just like the earthlings will have observed everything age, except for you. Remember that it took 27 billion years for them to watch you travel away (with only one day of aging) but then they see you coming back in just one day and they see you age just one more day. So when you get back, you are only two days older while they and everything else in the universe is 27 billion years older.
It wouldn't just seem like a few seconds, it would actually be just a few seconds. But let me just add again that the earthlings would see that it took 40 minutes for you to get to Mars during which time they would see that your clock had advanced by just one second, then they would see that you stayed there for a few seconds and on the return trip, they would see you take just a second to return so they would see you age four seconds during your trip while their own clocks advanced by a little over 40 minutes.
The number of revolutions is the same. If your son sees you go around the earth Y number of times and you see him go around you X number of times, then X and Y are equal. How could it be otherwise?

16. Jun 7, 2012

### yuiop

In the FAQ on the experimental evidence for relativity and the clock postulate section http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Clock_Hypothesis it states:

"The clock hypothesis states that the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives. The experiment of Bailey et al. referenced above stored muons in a magnetic storage ring and measured their lifetime. While being stored in the ring they were subject to a proper acceleration of approximately 1018 g (1 g = 9.8 m/s2). The observed agreement between the lifetime of the stored muons with that of muons with the same energy moving inertially confirms the clock hypothesis for accelerations of that magnitude."

10^18g is extreme and would liquidise any human being and yet the experiment demonstrated that the lifetime of the muons was time dilated only by the gamma factor for the instantaneous velocity (about 0.9994c) as if the particles were moving inertially in a straight line. The extreme centripetal force acting on the muons had no time dilation effect over and above the time dilation calculated for motion in a straight line. This is experimentally proven.

17. Jun 8, 2012

### uniqueland

So then basically I would see the train station going by at what the amount of revolutions would be if I were traveling at just under light speed for 30 years, even though my watch onboard my light speed train would only show that I had been on the train for a few hours so it would seem to me as if the train were traveling a much higher speed than just light speed, figuring that it would take me one whole light second to make say around 6 revolutions around the planet. but I would "see" (putting aside for my example any consideration that it would be impossible for me to actually make out what I would be seeing even without my view outside being accelerated for me) that train station passing by thousands or millions of times greater per second than just 6 because everything outside would be accelerated proportionate to the degree to which time slowed down for me. Conversely, if my son at the train station were looking at a monitor hooked up to a video camera focused on me onboard the train, it would seem as if I was frozen in place since it might take me a month just to blink my eyes from his perspective. Is that correct?

18. Jun 9, 2012

### ghwellsjr

No, it won't seem to you that you are traveling faster than light speed. As I said in post #13, you're overlooking length contration. And HallsofIvy explained this way back in post #4:
In other words, you would determine that the distance around the earth was much shorter than your son would determine it to be.
Yes.

19. Jun 11, 2012

### uniqueland

Then my son at the train station viewing an webcam onboard my light speed train would see me as all but frozen with it taking maybe a month for me to make a smile whereas me viewing a webcam of the train station would show people moving around in a complete blur because I would see them moving speeded up by thousands of times the actual earth speed. Right?

20. Jun 11, 2012

### ghwellsjr

Yes, on average, your son would see you in slow motion and you would see all the people in fast motion, but I wouldn't say "thousands of times actual earth speed", just thousands of times your speed.