# Infinite accelerations?

1. Jun 4, 2005

### apophis924

infinite accelerations???

My question is about time dialation. I know that as one approaches light speed time dialation occurs. Now this dialation of time is the result of accelarations. what happens if one maintains a constant speed of lets say 50% of C. once speed is constant wouldnt the effects of accelartion and gravity return to zero? If so would time dialation also cease? I know once you take off on a commercail airliner one feels G accelrations but once altitude is reached one hardly feels movement or any significant G forces. Does the same thing apply for time dialation once a ship reaches and sustains a constant speed regardless of what % of C it is?

2. Jun 4, 2005

### pervect

Staff Emeritus
No, time dilation is caused by velocity, not acceleration. Actually there are a couple of forms of time dilation, but the sort due to motion is due to motion (velocity).

The formula for this is

tau = 1/sqrt(1-v^2/c^2)

so that at 50% of the speed of light, the time dilation factor is 2/sqrt(3).

3. Jun 5, 2005

### HallsofIvy

Staff Emeritus
Time dilation is, also, relative to some other frame of reference. A body moving at 1/2 the speed of light relative to some other frame of reference would appear to be time-dilated to observers in that other frame of reference. Observer's in the speeding body would see no time dilation, since an observer always has speed 0 in his own frame of reference. In fact, such an observer would see the others as time-dilated.

4. Jun 5, 2005

### Danger

This is something that has always puzzled me, perhaps just because of not knowing any math. As I understand it, one's own inertial frame is always considered to be the stationary one relative to the rest. In that case, how does one determine which of the twins in the famous paradox actually undergoes slower aging? Why wouldn't they see each other as being dilated, and wind up the same when they meet again? What about an observer from a 3rd frame?

5. Jun 5, 2005

### quetzalcoatl9

this has always puzzled me as well...

can anyone respond to this?

6. Jun 5, 2005

### Garth

The one who does not remain in an inertial frame of reference. This is because acceleration affects the 'plane of simultaneity' of that observer, both on the way out, on the U turn and on deceleration on return.

The two twin observers are not in equivalent frames of reference, one is inertial and the other not, therefore it is possible to distinguish between them. There have been endless posts on this subject in these Forums.

Garth

Last edited: Jun 5, 2005
7. Jun 5, 2005

### Janus

Staff Emeritus
You have to take two other effects into account: length contraction and Relativity of Simultaneity.

Length contraction will cause one of the twins to measure the distance traveled as shorter. (generally the distance traveled is as measured by the twin we assign as the "stationary" twin.) Thus, if the stationary twin measures the distance traveled by his brother as 1 ly at .866c, his brother will measure that distance as .5 ly. Thus one of the twins will record a shorter trip time than the other.

Relativity of Simultaneity means that the two twins will not agree as to what events are simulatanteous. Thus clocks that are perfectly synchronised in one frame will not be seen as so from the other.

Imagine that you have a clock on the On the Earth and at the turn around point that show exactly the same time according to the Earth. To the twin traveling out to the turn around point, the clock at the turn around point will show a later time than the Earth clock. When he gets to the turn around around point he brakes to a stop and starts back to Earth. Assuming that he stays relatively close to the turnaround clock, its time pretty much stays the same. But now that he is heading back towards the Earth, it is the Earth clock which shows a later time than the turnaround clock. This means that he will measure the Earth clock as running very fast during the time he does his turn around.

The Earth twin however never sees his brother's clock as running fast, only slow.

Thus the Earth twin says his brother aged less because time ran slower for his brother.

While the "traveling" twin says that while his brother aged slower for most of the trip, during the time he was making his turn around,his brother aged very rapidly, so that by the time they got back together his brother had aged less.

The trick here is that one of the twins has to undergo an acceleration at the point of maximum separation of the two brothers in order for them to meet again, and it is this twin that will have accumulated the least time when they meet again.

8. Jun 27, 2005

### Danger

Thanks for the explanation. Also to Garth. Sorry it took so long to get back here. (I forgot where I'd posted it. )