Exploring Time Dilation: The Effects of Constant Speed on Infinite Accelerations

  • Thread starter apophis924
  • Start date
  • Tags
    Infinite
In summary, time dilation is caused by velocity, not acceleration, and is relative to the frame of reference of the observer. The formula for time dilation is tau = 1/sqrt(1-v^2/c^2), and at 50% the speed of light, the time dilation factor is 2/sqrt(3). In the famous twin paradox, the twin who does not remain in an inertial frame of reference will experience slower aging due to acceleration affecting the 'plane of simultaneity'. This is because of the effects of length contraction and Relativity of Simultaneity. The two twins will not agree on what events are simultaneous, and therefore will not age the same.
  • #1
apophis924
1
0
infinite accelerations?

My question is about time dialation. I know that as one approaches light speed time dilation occurs. Now this dilation of time is the result of accelarations. what happens if one maintains a constant speed of let's say 50% of C. once speed is constant wouldn't the effects of accelartion and gravity return to zero? If so would time dilation 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 dilation once a ship reaches and sustains a constant speed regardless of what % of C it is?
 
Physics news on Phys.org
  • #2
apophis924 said:
My question is about time dialation. I know that as one approaches light speed time dilation occurs. Now this dilation of time is the result of accelarations. what happens if one maintains a constant speed of let's say 50% of C. once speed is constant wouldn't the effects of accelartion and gravity return to zero? If so would time dilation 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 dilation once a ship reaches and sustains a constant speed regardless of what % of C it is?

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
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
HallsofIvy said:
In fact, such an observer would see the others as time-dilated.
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
Danger said:
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?

this has always puzzled me as well...

can anyone respond to this?
 
  • #6
how does one determine which of the twins in the famous paradox actually undergoes slower aging?
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:
  • #7
Danger said:
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?
You can't, at least not in terms of who is aging slower at any given point in any absolute sense. But you can determine who accumulates the least amount of total time during the duration of the trip.
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?

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
Janus said:
You have to take two other effects into account: length contraction and Relativity of Simultaneity.
Thanks for the explanation. Also to Garth. Sorry it took so long to get back here. (I forgot where I'd posted it. :redface: )
 

1. What is time dilation?

Time dilation is a phenomenon in which time appears to pass slower for an object or person moving at a constant speed compared to those at rest. This is a consequence of Einstein's theory of relativity.

2. How does constant speed affect time dilation?

As an object or person moves at a constant speed, they experience time dilation because their velocity is changing at a constant rate. The faster the speed, the more time appears to slow down for the moving object.

3. What is the relationship between time dilation and infinite accelerations?

Time dilation and infinite accelerations are closely related. As an object approaches infinite acceleration, time appears to slow down to a near halt. This is because the object's velocity is changing at an extremely fast rate, causing significant time dilation.

4. How is time dilation measured?

Time dilation can be measured using precise clocks and comparing the time experienced by the moving object with the time experienced by a stationary object. This can also be observed in experiments involving fast-moving particles and their decay rates.

5. What are some real-world examples of time dilation?

Some examples of time dilation in the real world include the time dilation experienced by astronauts in space, the GPS system correcting for time dilation in satellites, and the time dilation observed in particle accelerators.

Similar threads

  • Special and General Relativity
Replies
25
Views
536
Replies
35
Views
1K
  • Special and General Relativity
Replies
2
Views
875
  • Special and General Relativity
Replies
4
Views
1K
  • Special and General Relativity
3
Replies
70
Views
3K
  • Special and General Relativity
Replies
5
Views
1K
  • Special and General Relativity
4
Replies
115
Views
5K
  • Special and General Relativity
2
Replies
65
Views
4K
Replies
130
Views
7K
  • Special and General Relativity
Replies
3
Views
1K
Back
Top