# Time dilation

#### O Great One

Imagine the following scenario:
Persons A and B are situated like so:

A
<--------C
B

There is a gun at C which is firing one bullet per second (from the reference frame of A) directly between A and B. They each observe the bullets passing between them. Imagine person B is undergoing time dilation relative to person A. We immediately run into problems. One of the following two scenarios must result:

1) When A and B are asked how many bullets have passed them, they give the same number as an answer. That's not possible if time for person B is passing at a different rate. For example, if time is passing at half the rate for B, he should only observe half the number of bullets as A did.

2) A and B give different answers. How is that possible since the bullets are coming from the same gun?

This situation is directly analogous to two people inside of a tall building, one on top, the other on the ground floor. If time for the person on the top is passing more quickly then everything is speeded up, including the motion of the sun through the sky. Eventually, the person on top will be a day, then a week, then a month ahead. He will therefore observe more sunsets and sunrises than the person on the bottom. But how is that possible if they are fixed at the same location on Earth?

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#### maximus

Originally posted by O Great One
1) When A and B are asked how many bullets have passed them, they give the same number as an answer. That's not possible if time for person B is passing at a different rate. For example, if time is passing at half the rate for B, he should only observe half the number of bullets as A did.
hm. i think that after a fixed amount of time they would actually report the same number of bullets. the difference between the two is that chemical/brain reactions would be slower (or is it faster? this is an interesting question!) for person B and therefore the bullets would appear to be moving slower (or faster?), but the same amount would pass in the same amount of time. which ever way it is- faster or slower- i feel i'm right about my answer that the only difference would be the speed at which chemical reactions took place in the brain, and the speed at which the witnessed the same amount of bullets going by.

2) A and B give different answers. How is that possible since the bullets are coming from the same gun? [/B]
i feel that this is an immpossbile scererio to accept, so there must be another explanation.

#### Tyger

Let's take the tall building

and imagine a strobe light flashing on a middle floor level. If both observers used clocks that worked the same, e.g. atomic clocks, the top observer would see fewer flashes per unit time and the bottom one more. But the bottom one's day would appear to be shorter, measured by his clock time, and the top one's longer. And the "day" measured at the middle level would be somewhere in between.

#### O Great One

Originally posted by Tyger
If both observers used clocks that worked the same, e.g. atomic clocks, the top observer would see fewer flashes per unit time and the bottom one more.
This would be true if the clock for the observer on top was running faster, but time itself were passing at the same rate. Just like I can have a clock that runs twice as fast, but time itself is still passing at the same rate. If time were passing more quickly for the observer on top, then his clock would be running faster than the observer on the bottom and he would observe the same number of flashes per unit time as the person on the bottom. But this leads us into the problem I've mentioned above. At some point in time they will each have observed a different number of flashes, but how can they if it's coming from the same strobe light?

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#### Tyger

The two clocks

run just as fast when they are on the same floor of the building, but when they are separated they do in fact run at different speeds. When you carry the clock up a level you do work, which means you put energy into the clock. That energy means that all the electrons and nuclei of the clock have a slightly greater rest energy and quantum mechanical frequency than before, and proportionaly the clock runs faster.

That is one way of looking at it.

#### LURCH

Originally posted by O Great One
Imagine the following scenario:
Persons A and B are situated like so:

A
<--------C
B

There is a gun at C which is firing one bullet per second (from the reference frame of A) directly between A and B. They each observe the bullets passing between them. Imagine person B is undergoing time dilation relative to person A. We immediately run into problems. One of the following two scenarios must result:

1) When A and B are asked how many bullets have passed them, they give the same number as an answer. That's not possible if time for person B is passing at a different rate. For example, if time is passing at half the rate for B, he should only observe half the number of bullets as A did.

2) A and B give different answers. How is that possible since the bullets are coming from the same gun?

Time dilation predicts a third answer:

3) A and B give the same answer for the number of bullets that have gone by, but different answers as to how much time has passed.

If time dilation is extreme, A's time may be passing twice as quickly as B's. So A will say, "the gun has fired one bullet/second for a period of 10 seconds; a total of 10 bullets" while B would describe the same situation as, "the gun fired at a rate of 2 b/s for 5 seconds; a total of 10 bullets".

#### Janus

Staff Emeritus
Gold Member
Originally posted by O Great One

This situation is directly analogous to two people inside of a tall building, one on top, the other on the ground floor. If time for the person on the top is passing more quickly then everything is speeded up, including the motion of the sun through the sky.
No, the sun the motion of the sun across the sky is a external to the time rate experienced by either person. The person at the top will measure the time it takes for the sun to cross the sky as longer than that measured by the person at the bottom.

Eventually, the person on top will be a day, then a week, then a month ahead. He will therefore observe more sunsets and sunrises than the person on the bottom. But how is that possible if they are fixed at the same location on Earth?
This depends on how you measure a 'day", 'week' or 'Month' If you measured them by the movement of the sun, then both would measure the same number. Though each time period would be longer for the person at the top, as measured by any time keeping method he has locally with him ( A solar day may last 86401 sec rather than 86400 sec.)

If you mean a "day" as in 86400 sec measured by the local time, Then the observer at the top will measure more "standard" days, in any given time period. But the movement of the Sun across the sky won't match the length of this day. ( the Sun might appear to take 1.000011574 "days" to complete one circuit around the sky.)

#### O Great One

Clock faster, not time

Time dilation predicts a third answer:

3) A and B give the same answer for the number of bullets that have gone by, but different answers as to how much time has passed.

If time dilation is extreme, A's time may be passing twice as quickly as B's. So A will say, "the gun has fired one bullet/second for a period of 10 seconds; a total of 10 bullets" while B would describe the same situation as, "the gun fired at a rate of 2 b/s for 5 seconds; a total of 10 bullets".
What you have just described is not time dilation. Time is moving at the same rate for both of them but A's clock is running twice as fast as B's clock.

If you mean a "day" as in 86400 sec measured by the local time, Then the observer at the top will measure more "standard" days, in any given time period. But the movement of the Sun across the sky won't match the length of this day. ( the Sun might appear to take 1.000011574 "days" to complete one circuit around the sky.)
Again, you have just described a situation where the clock for the person on top is running faster than the person on the bottom, but time is passing at the same rate for both of them.

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#### LURCH

Re: Clock faster, not time

Originally posted by O Great One
What you have just described is not time dilation. Time is moving at the same rate for both of them but A's clock is running twice as fast as B's clock.

Again, you have just described a situation where the clock for the person on top is running faster than the person on the bottom, but time is passing at the same rate for both of them.
No, not just the clock, everything. For an outside observer, B's clock is moving half the speed of A's, but his heart is also beating at half the rate. If the two start out with syncronised clocks, and B measures his pulse to be 1 beat per second, then B steps into an area of space where time is dilated, he will still measure his pulse to be 1 b/s. His heart has slowed as much as his watch. Same goes for his respiration, the speed at which electrical pulses travel through his neural tissues, the rate at which his hair grows. All motion in the vacinity of B has slowed from an outsider's viewpoint. Of course, for B himself, his movement through time has remained the same, and everyone else has spead up.

#### O Great One

Clock faster, not time.

Let's state that B's heart is beating at a rate of 1 beat per second. Let's also state that time for B is going half as fast as A's time. Then in 10 seconds B will count 10 beats. Those 10 seconds will be equal to 20 seconds for A. A will count 20 beats coming from B, also 1 beat per second. If the 11th beat (for B) doesn't occur and B has a heart attack and dies then how many times did his heart beat? How can one answer this?

Before everybody starts saying that A will count 10 beats in 20 seconds. Let's imagine the following situation: A has a defective watch that runs twice as fast as B's watch. B notes that his heart beats 10 times in 10 seconds. A notes that B's heart beats 10 times in 20 seconds. A's watch is going twice as fast as B's watch but time is passing at the same rate for both of them.

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#### Janus

Staff Emeritus
Gold Member
Re: Clock faster, not time.

Originally posted by O Great One
Let's state that B's heart is beating at a rate of 1 beat per second. Let's also state that time for B is going half as fast as A's time. Then in 10 seconds B will count 10 beats. Those 10 seconds will be equal to 20 seconds for A. A will count 20 beats coming from B, also 1 beat per second.
No, A will count 20 beats at .5 beats per sec.

If the 11th beat (for B) doesn't occur and B has a heart attack and dies then how many times did his heart beat? How can one answer this?
Ten beats.

Before everybody starts saying that A will count 10 beats in 20 seconds.
Since this is the correct answer, why shoudn't we?

[/b]
Let's imagine the following situation: A has a defective watch that runs twice as fast as B's watch. B notes that his heart beats 10 times in 10 seconds. A notes that B's heart beats 10 times in 20 seconds. A's watch is going twice as fast as B's watch but time is passing at the same rate for both of them. [/B]
Bringing defecticve clocks into the scenerio does nothing towards erudition in this example.

When working with clocks in Relativity problems such as this, it is an automatic condition that the clocks are of identical construction. The very word "clock" in such problems merely stands for "a means to accurately measure local time."

#### LURCH

Re: Clock faster, not time.

Originally posted by O Great One
Let's imagine the following situation: A has a defective watch that runs twice as fast as B's watch. B notes that his heart beats 10 times in 10 seconds. A notes that B's heart beats 10 times in 20 seconds. A's watch is going twice as fast as B's watch but time is passing at the same rate for both of them.
In this scenario, A will also notice that his own heart is beating half as fast as it was at the beginning of the experiment (when their clocks were in sync). Same goes for his respiration, the speed at which elctrical pulses travel through his neural tissues, the rate at which his hair grows, ect. Time is not faster in the vacinity of A, only his clock is accelerated. His hair growth, speed of thought, the time ti takes his eyelids to blink, the rate at which he sees a pin drop, are all still in sync with B.

#### Hurkyl

Staff Emeritus
Gold Member
1) When A and B are asked how many bullets have passed them, they give the same number as an answer. That's not possible if time for person B is passing at a different rate. For example, if time is passing at half the rate for B, he should only observe half the number of bullets as A did.

2) A and B give different answers. How is that possible since the bullets are coming from the same gun?
You've confused yourself by an ambiguity in your problem. You haven't specified how A and B measure bullets. I see two possible ways to finish stating your problem, and each of your answers is the right answer for one of those ways.

In particular, you have not specified how the bullets are to be counted. There are two easy ways I can see to do this:

(1) At some point in time, observer C shouts "NOW!" and then 10 bullets later, C shouts "STOP!". Observer A and B will both count 10 bullets. Observer A thinks 10 seconds has elapsed between "NOW" and "STOP", consistent with observer A's observation that the gun is being fired at 1 bullet per second. However, that rate was A's observation. Because time is moving half as fast for B as it was for A, B thinks only 5 seconds have passed, and that the gun was being fired at 2 bullets per second.

(2) A and B agree to count bullets for 10 seconds. A thinks that the gun is being fired at 1 bullet per second, so A counts 10 bullets. B thinks the gun is being fired at 2 bullets per second, so B counts 20 bullets. However, A and B don't start and stop at the same time; in particular A thinks B has been counting for 20 seconds, while B thinks A stopped after 5 seconds. Whichever reference frame you consider, B has been counting twice as long with A.

I think you confused yourself into thinking that both A and B are starting and stopping at the same time, yet A and B are counting for the same amount of time (an impossibility of A and B are experiencing time dilation with respect to each other)

#### physicskid

Besides time dilation, do not forget about length contraction and you did not state that if B is undergoing time dilation due to what(motion or gravity?). If B is moving towards to C, The bullets would appear to move faster. So it's better to say that C is emitting a photon/sec.

When B undergoes time dilation, the surrounding that B observe would contract due to length contraction, but he would not be able to notice that becos he shrinks as well. Let's say if the lenght contracts by 50%, the watch on B would also move faster by 50%. So to B the speed of the photon is the same because the photon only has to travel 1/2 the distance.

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#### O Great One

Clock faster, not time

Perhaps I need to add to my example to clarify my point: Speeding up a clock does not speed up time. Speeding up a clock and speeding up time are getting confused with each other. Let's try again:

Let's state that B's heart is beating at a rate of 1 beat per second. Let's also state that time for B is going half as fast as A's time. Then in 10 seconds B will count 10 beats. Those 10 seconds will be equal to 20 seconds for A. A will count 20 beats coming from B, also 1 beat per second.

Before everybody starts saying that A will count 10 beats in 20 seconds let's imagine the following situation:
There is a friend of B's called C for whom time is passing at the same rate as B. C has a defective watch which runs twice as fast as B's watch. Remember, C's watch is going twice as fast B's watch but his time is going at the same rate.
B notes that his heart beats 10 times in 10 seconds.

C notes that B's heart beats 10 times in 20 seconds.<- watch faster!

A notes that B's heart beats 10 times in 20 seconds.<- time dilation?

How can we claim that A is undergoing time dilation when his results are the same as somebody whose watch is moving faster, but time is passing at the same rate?

#### Hurkyl

Staff Emeritus
Gold Member
Speeding up a clock does not speed up time.
However, speeding up time does speed up a clock. (from an external reference point)

How can we claim that A is undergoing time dilation when his results are the same as somebody whose watch is moving faster, but time is passing at the same rate?
Because we can take everybody's watch and bring them all to the same place in space-time (so there will be no more time dilation). We can then measure how everybody's watch is synchronized. In particular, we will then see that C's watch is still running twice as fast as B's, but A's watch is now running the same speed as B's. We then know that C just had a defective watch and A was experiencing time dilation with respect to B.

#### Tyger

Re: Clock faster, not time

Originally posted by O Great One
Perhaps I need to add to my example to clarify my point: Speeding up a clock does not speed up time. Speeding up a clock and speeding up time are getting confused with each other. Let's try again:
How do you give meaning to the notion of "speeding up time"? Time is something we measure with clocks. The only time we know is experiential time, what Einstein calls proper time. This puzzles me.

#### Janus

Staff Emeritus
Gold Member
Re: Clock faster, not time

Originally posted by O Great One

How can we claim that A is undergoing time dilation when his results are the same as somebody whose watch is moving faster, but time is passing at the same rate?
But the results aren't the same. As already pointed out, the clocks can be brought together and compared.

Besides, C can compare his watch to local events. If he compares it to his own heart beat, he will also get 10 beats in 20 seconds, even though he knows that his heart is beating at a normal rate and not at half speed.

With time dialtion, your clock will always be in sync with your local environment. It will be out of sync, however, with the clock and environment that you are noting the time dialtion in. (this clock and environment will be in sync with each other.)

#### Zantra

Originally posted by O Great One
Imagine the following scenario:
Persons A and B are situated like so:

A
<--------C
B

There is a gun at C which is firing one bullet per second (from the reference frame of A) directly between A and B. They each observe the bullets passing between them. Imagine person B is undergoing time dilation relative to person A. We immediately run into problems. One of the following two scenarios must result:

1) When A and B are asked how many bullets have passed them, they give the same number as an answer. That's not possible if time for person B is passing at a different rate. For example, if time is passing at half the rate for B, he should only observe half the number of bullets as A did.

2) A and B give different answers. How is that possible since the bullets are coming from the same gun?

This situation is directly analogous to two people inside of a tall building, one on top, the other on the ground floor. If time for the person on the top is passing more quickly then everything is speeded up, including the motion of the sun through the sky. Eventually, the person on top will be a day, then a week, then a month ahead. He will therefore observe more sunsets and sunrises than the person on the bottom. But how is that possible if they are fixed at the same location on Earth?
Simple. If time is passing slower for one person that the other, then then the person affected by time dialation will have observed less bullets simply because for him, the event of the missing bullets has not occured yet. We're assuming that for the shooter and person B, time is moving at a normal rate of speed while time is moving slower for person A.

If time moves slower, then the events occur at a different rate of speed. Assuming person B sees 10 bullets, and person A sees only 5, this simply means that for person A, the remaining 5 bullets have not occured yet, relative to his perception of the shooter.

As for the sun analogy, We first have to ask, how is it that time is moving differently for the person on top then the person on the bottom? If they are each experiencing 2 different rates of time, then that inof itsself is an anomoly. It's analagous to that movie "time machine" where he's travelling through time in his little bubble, watching the years speed by around him. I believe it would be much the same experience for any time traveller where he to do so with a transparent bubble, and be able to watch the external world around him. Of course that's a movie.. heheh

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