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# Time dilation does not make sense to me.

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So according to relativity the faster an object is moving relative to another object - the slower the moving objects time flows relative to the stationary object. This is called time dilation.

Well lets say I am on a rock in space and there is a space ship flying by me near the speed of light. We both are reading a book for about 5 minutes. Lets say that in that 5 minutes I can read 15 pages of the book. The guy in the space ship also reads 15 pages in 5 minutes. But because of him moving that fast if I look at him - his time will be flowing slower, so I would be able to read the 15 pages in the given 5 minutes while he will be at... let say the 2-nd page after 5 minutes. So the conclusion would be that I read 15 pages in 5 minutes, while he read only 2, because of him moving so fast. But now lets switch paces. I am now on the ship and that guy... err... Derrick is now on the rock. So I am moving close to c past him, but from my perspective he is the one speeding and reading slower. So after the 5 minutes of reading on the ship I will be on page 15, while he still is on page 2. Nope... does not make sense at all...

And btw if I look at a speeding object I will see it "living" in slow motion. Well let's say that the speeding object is looking back at me - shouldn't he see the opposite - me "living" very fast? No he because relative to him I am the one speeding and in slow motion, but how can both observers see the other one in slow motion? One must see the other moving very fast for the other to see one moving very slow for this to make sense... but according to time dilation and relativity, there actually won't be anyone anyone "living" very fast.

Very-very confusing.

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One thing about Relativity is that to wrap your mind around it you have to drop some preconceptions on the nature of "time".

I'll try to clear things up by using an analogy.

Imagine two men walking, and "time" is the distance stretching out in front and behind them. The distance they have walked is how far they have progressed in time.

So your question is: How can both men see the other as walking more slowly then he is? It would seem that no matter how you cut it, the men should agree as to who is walking faster.

But, consider what happens if the men walk at an angle to each other. (We can assume that they start at the same point and walk at the same speed. )

If each man judges progress through time as the distance he has traveled in the direction that he himself is walking. Then it is obvious that each man will determine that the other man is making less progress (he has to look back over his shoulder to see the other man).

This is how time behaves, Two people traveling at different speeds measure time differently, each measures himself as making better progress through time.

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ALso, you take your paradox away if you consider not 5 min in your reference frame for both, but for you the 5 min in your frame and for Derrick you apply the transformation and calculate how much willbe 5 miin for him in your frame and then you'll see you both read 15 pages...

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Ok, so lets say I am on the rock and the ship is moving past me at close to c jet again. So lets say that it takes Derrick 5 minutes to move from point A to point B. So I am on the rock and as soon as he bypasses point A I start to read. When he reaches point B I stop and what do you know - I am on page 15, because I had 5 minutes to read, but Derrick is still on page 2, because of time dilation. Well.. now I am on the ship and Derrick on the rock. Let's do it again. I pass point A and start to read. Finally after 5 minutes I reach point B (because as I mentioned before it takes 5 minutes for the ship to move from point A to point :shade: and I seem to be on page 15, but Derrick on the rock is still on page 2, because in reference to me he was the one speeding and his time was flowing slower.

So the problem here is: When the ship reached point B, how can Derrick on the rock still be on page 2 and me on the ship on page 15, while if I was on the rock and the ship reached point B I would be on page 15 and he still on page 2?

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And btw if I look at a speeding object I will see it "living" in slow motion. Well let's say that the speeding object is looking back at me - shouldn't he see the opposite - me "living" very fast? No he because relative to him I am the one speeding and in slow motion, but how can both observers see the other one in slow motion?

Very-very confusing.

Both observers see one another living in slow motion. It is confusing – or at least counter-intuitive.

There are many ways to clear up the confusion, which results, I believe, from a failure to appreciate that, when dealing with fast moving objects, they not only move fast, but go far, and when dealing with far distances, intuitive ideas like “at the same time” become more complicated.

Rather than learning to perceive the situation in terms a space-time coordinate transforms – a good approach, but not a quick nor easy one - you might try coming up with a simple model of how the 2 observers can “see” one another, then write everything of relevance about it in a table. For example:

Assume things work like this: The person on the rock and the person on the ship both have a simple stop-watches that read-out in seconds, and gadgets similar to a camera flash, but powerful enough to be seen at interplanetary distances. They also have notepads and pencils (or good memories) to note when they see each others flashes. The ship has a super-engine that accelerates it to 60% the speed of light in a fraction of a second. Each person agrees that he will trigger his flash every 60 seconds after the ship is launched, and recording the time on his watch when he sees the other’s flash. This gives them each a picture of how fast the other is living. When they’ve each sent and received four flashes, they’ll somehow compare results (how isn’t important – any sort of radio would work).

All we need know how to simulate this experiment is how to calculate the time dilation factor for a speed of .6 c, $\sqrt{1 - .6^2} = .8 \, \mbox{c}$, using the Lorentz formula. The rest is just arithmetic, and gives a table like this:

                  Signal locations
Base- Ship- Base- Ship- Base- Ship- Base- Ship-
Base  Ship  Ship  Ship  Base  Ship  Base  Ship  Base  Ship  Base
time  Time  Loc.  #1    #1    #2    #2    #3    #3    #4    #4
(s)   (s)   (ls)  (ls)  (ls)  (ls)  (ls)  (ls)  (ls)  (ls)  (ls)
0     0     0
60    48    36    0
75    60    45    15    45
120*  96    72    60    0     0
150   120*  90    90          30    90
180   144   108               60    60    0
225   180   135               105   15    45    135
240*  192   144               120   0     60    120   0
300   240*  180               180         120   60    60     180
360*  288   216                           180   0     120    120
450   360*  270                           270         210    30
480*  384   288                                       240    0
600   480*  360                                       360

Note that, to keep things simple, units of light-seconds (ls) are used for location measurements. A light-second is about 300,000,000 meters. An “*” next to the clock reading indicates when each flash signal is received.

Note that the table shows each observer sees the other living at exactly 50% normal speed. If they do the math to compensate for the time required for each signal flash to reach them, they’ll adjust that rate to 80%, but both will still see the other living in slow motion.

We left the 2 observers drifting apart at .6 c, never to be reunited. To really make sense of what’s going on, we need to extend the experiment a bit, and bring them back together. They’ll be able to compare clocks up close and personal, where we no longer need to pay attention to how they do it by tracking each signal passed between them. Depending on how they get back together, they’ll find that less time has passed on one watch than on the other, without any paradoxical difficulty deciding which one.

Expanding the table is left as an exercise to the reader. I recommend using the ship’s miracle motor reverse its velocity to .6 c in the opposite direction, then using it one more time to bring it to a dead halt back on the base rock (the calculations work out in nice whole numbers using a speed of .6 c).

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Ok, so lets say I am on the rock and the ship is moving past me at close to c jet again. So lets say that it takes Derrick 5 minutes to move from point A to point B. So I am on the rock and as soon as he bypasses point A I start to read. When he reaches point B I stop and what do you know - I am on page 15, because I had 5 minutes to read, but Derrick is still on page 2, because of time dilation. Well.. now I am on the ship and Derrick on the rock. Let's do it again. I pass point A and start to read. Finally after 5 minutes I reach point B (because as I mentioned before it takes 5 minutes for the ship to move from point A to point :( and I seem to be on page 15, but Derrick on the rock is still on page 2, because in reference to me he was the one speeding and his time was flowing slower.

So the problem here is: When the ship reached point B, how can Derrick on the rock still be on page 2 and me on the ship on page 15, while if I was on the rock and the ship reached point B I would be on page 15 and he still on page 2?

Here's the thing: You also have to take length contraction into account. The distance between A and B will depend on whether it is measured from the rock or the ship. From your description I'll assume that A nd B are at rest with respect to the rock. (assume that there are two other rocks at rest with respect to the frst rock sitting at those two points.) Thus these two points are moving when measured from the ships perspective, and undergo length contraction, A and B will be closer together then as measured from the rock. While you are on the ship it will take less time from the instant that A passes till B passes because of the shorter distance between the two, and you will only be on page two when you pass point B.

Now comes the part that a lot of people have trouble wrapping their mind around, it is called the "Simultaneity of Relativity"

It turns out that two people traveling at relative speed to each other will not always agree as to which events happen at the same time.

To illustrate, Let's put two more people into the situation, one each sitting at A and B. They also have books. By arrangement, they both start reading the instant the person on the first rock does. (as determined by them and the person on the first rock. )

Therefore, according to them, the ship passes point A, and everyone starts reading. It passes point B and everyone stops reading. So when the ship passes point B the reader at point B has reached page 15.

Now from the ship's point of view: the man at point A starts reading as point A passes, But The man at point B had started reading already and by this time is quite a ways into page 14. In the time that take for point B to pass( and for the person in the ship to read 2 pages), the man at point B finishes page fourteen and starts page fifteen.

While the three readers on the rocks all agree that they started reading at the same moment, the reader in the ship will not agree, but will say that reader B started reading before reader A.

The upshot is that everyone agrees the reader on the Ship starts reading as he passes A and that the reader at A starts reading at the same moment. They will also agree the the reader at B will be on page 15 when the ship passes A, and that the reader on the ship will be on page 2.

This goes back to what I said about having to lose preconceptions on the behavior of time. The fact the "at the same time" depends on relative motion is not an easy idea to digest.

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Very informative, thank you. I'll try to get my mind around this.

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• 2 weeks later...

This is by the most confusing topic on science, I think. Because most of us are conditioned or taught to think that time is the same for everyone.

Either way, what evidence is there for this being true? To test it you need to have objects traveling at least 5% of light speed, and I mean vehicles and/or ships, to have persons experimenting this... not particle acceleration.

And so far, what's the highest speed a traveling object has reached?

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Well actually there have been successful tests on this, but the difference was recorded in only mere nanoseconds. Still it's a difference.

Here is a test to prove it:

Now if anyone knows someone that has tested this but using something faster than just an airplane. Something more like a shuttle?

And I myself am also interested in finding out the fastest we have gotten something to move that can carry passengers. I would assume a rocket in orbit. (how fast does a rocket move in orbit anyway?)

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Well actually there have been successful tests on this, but the difference was recorded in only mere nanoseconds. Still it's a difference.

Here is a test to prove it:

Now if anyone knows someone that has tested this but using something faster than just an airplane. Something more like a shuttle?

You might look at the adjustments that need to be made to our satellites (like mobile phone and GPS).

Also, thanks for sharing the YouTube link above, Agen. If I'm not mistaken, that was part of a PBS special (that I actually own on video):

NOVA Online | Time Travel

Cheers. :eek2:

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Agen

Well actually there have been successful tests on this' date=' but the difference was recorded in only mere nanoseconds. Still it's a difference.

Here is a test to prove it:

Now if anyone knows someone that has tested this but using something faster than just an airplane. Something more like a shuttle?

And I myself am also interested in finding out the fastest we have gotten something to move that can carry passengers. I would assume a rocket in orbit. [b'](how fast does a rocket move in orbit anyway?[/b]) [/Quote]

According to the 2001 Guinness World Records Apollo 10 has the record for the highest speed attained by a manned vehicle: 39' date='897 km/h (11.08 km/s or 24,791 mph). The speed record was set during the return from the Moon on 26 May 1969. [/Quote']

Still looking;)

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And so far, what's the highest speed a traveling object has reached?
Particle accelerators routinely accelerate protons or electrons to speeds greater than .999 c. Though it’s difficult to put a clock on a proton ;), accelerator experiments have observed the rate of decay of short-lived particles resulting from collisions being time dilated by large factors.

This ucr.edu-hosted page has a good list of the many experimental verification of Special Relativity.

According to the 2001 Guinness World Records Apollo 10 has the record for the highest speed attained by a manned vehicle: 39,897 km/h (11.08 km/s or 24,791 mph). The speed record was set during the return from the Moon on 26 May 1969.
Still looking;)
I believe the fastest speed of any spacecraft relative to the Earth, Sun, etc., was about 252,792 km/h (.0002342 c), in 1976, by the second of the Helios probes. Per the usual formula, this would produce a time dilation factor of $\tau = \sqrt{1 - .0002342^2} \cdot= .999999972568$, or about .00237 seconds/day.

This Encyclopedia of Astrobiology, Astronomy and Spaceflight entry has many other spacecraft speed records.

With present-day spaceflight technology, the highest speeds obtainable by spacecraft will, I suspect, always be due to gravitational acceleration.

Consider the possible speed if the New Horizon’s probe were programmed to plunge directly from its 2017 Pluto flyby into the Sun. Give Pluto’s distance of about $r_1 = 4.7 \times 10^{12} \,\mbox{m}$, the Sun’s equatorial radius of $r_2 = 7 \times 10^8 \,\mbox{m}$, an initial velocity of the probe of about $47000 \,\mbox{m/s}$, and the equation for velocity just prior to striking or nearly striking the Sun $v_2 = \sqrt{ 2 \mu_{Sun} \left ( \frac1{r_2} - \frac1{r_1} \right ) +v_1}$, we calculate $v_2 \dot= 617536 \,\mbox{m/s} \dot= 2,223,132 \,\mbox{km/h} \dot= .00205 \,\mbox{c}$, and $\tau \dot= .999997878 \dot= .1833 \,\mbox{seconds/day}$ – well within the sensitivity of a good mechanical watch!

For the orbital mechanics fans at hypography, designing a mission to achieve maximum spacecraft velocity (via optimum programmed gravitational slingshot from the planets) is an interesting challenge.

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