### Patrick Bowman

Shared publicly -surya raju (+surya raju)

I'm not sure how you came to ask these questions of me, nonetheless I will have a go at addressing them.

Question 1

`Please explain about time dilation. Is it really possible to "travel with time " ?'

I'm not about to provide a course in Special Relativity (a good place to start would be: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/conrel.html#c1), but I think the fundamental point is this:

When Newton constructed his mechanics, he made the assumption that all observers will agree on measurements such as the distance between two points, and the time interval between two events. These were perfectly reasonable assumptions, but are, in fact, wrong.

The twin phenomena of length contraction (the faster a ruler is moving, the shorter it is) and time dilation (the faster a clock moves, the more slowly it ticks) work together so that all observers agree on speed.

For example, an observer on Earth measures the distance to Alpha Centauri to be 4 light years. So a spaceship travelling at half the speed of light would take 8 years to get there (from the point of view of an observer on Earth). Astronauts on the spaceship measure a shorter distance to Alpha Centauri (about 3.5 light years) and the travel time is correspondingly less (about 6.9 years), but they agree with observers on the ground that they are travelling at half the speed of light.

The effect has been thoroughly tested experimentally. Some of the more famous examples are the lifetime of atmospheric muons, the Hafele and Keating experiment where clocks were flown on planes, and the use of GPS. (The last two actually include an extra effect - gravitational time dilation.)

Question2.

`Earth is moving from one place to another place and rotating around the sun. Assume, In the earth one object is jumped (100m) strait 90 degrees at one particular point in 5 minutes and falls down at that "Same point" my doubt is how is it possible . because earth is rotating with some speed .

note : At 100th meter the object gravitational force is zero ,may be i right. my question is how is it possible?'

The precise motion of a projectile, from the point of view of an observer on the ground, is indeed complicated for the reasons you have mentioned. However, so long as the motion is over a relatively short distance and time, the motion of the Earth can be neglected. Here is why: whilst the tangential speed of the Earth's surface is quite large -- and the orbital speed of the Earth greater still -- the circumference of the Earth is large enough that the motion is in an approximately straight line over the time considered. That means that the observer can be used to define a stationary (and inertial) frame of reference. The problem then reduces to a straight-forward one of kinematics (http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html). In a sense, the observer and projectile are both equally affected by the Earth's motion (as they are when they are together on the ground), so it washes out of the problem.

As for the specific problem given, the travel time for an object being thrown straight up in the air to a height of 100m above ground, then returning to Earth is about 9 seconds. And the difference in acceleration due to gravity over that distance is negligible (the distance travelled is tiny compared to the Earth's radius).

If the time/distance travelled and the required precision of the measurement is such that the Earth's motion must be taken into account, this can be dealt with by inclusion of the so-called Coriolis force and Centrifugal force. But if you're worried about those effects, you should probably also be modelling air resistance.

I'm not sure how you came to ask these questions of me, nonetheless I will have a go at addressing them.

Question 1

`Please explain about time dilation. Is it really possible to "travel with time " ?'

I'm not about to provide a course in Special Relativity (a good place to start would be: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/conrel.html#c1), but I think the fundamental point is this:

When Newton constructed his mechanics, he made the assumption that all observers will agree on measurements such as the distance between two points, and the time interval between two events. These were perfectly reasonable assumptions, but are, in fact, wrong.

The twin phenomena of length contraction (the faster a ruler is moving, the shorter it is) and time dilation (the faster a clock moves, the more slowly it ticks) work together so that all observers agree on speed.

For example, an observer on Earth measures the distance to Alpha Centauri to be 4 light years. So a spaceship travelling at half the speed of light would take 8 years to get there (from the point of view of an observer on Earth). Astronauts on the spaceship measure a shorter distance to Alpha Centauri (about 3.5 light years) and the travel time is correspondingly less (about 6.9 years), but they agree with observers on the ground that they are travelling at half the speed of light.

The effect has been thoroughly tested experimentally. Some of the more famous examples are the lifetime of atmospheric muons, the Hafele and Keating experiment where clocks were flown on planes, and the use of GPS. (The last two actually include an extra effect - gravitational time dilation.)

Question2.

`Earth is moving from one place to another place and rotating around the sun. Assume, In the earth one object is jumped (100m) strait 90 degrees at one particular point in 5 minutes and falls down at that "Same point" my doubt is how is it possible . because earth is rotating with some speed .

note : At 100th meter the object gravitational force is zero ,may be i right. my question is how is it possible?'

The precise motion of a projectile, from the point of view of an observer on the ground, is indeed complicated for the reasons you have mentioned. However, so long as the motion is over a relatively short distance and time, the motion of the Earth can be neglected. Here is why: whilst the tangential speed of the Earth's surface is quite large -- and the orbital speed of the Earth greater still -- the circumference of the Earth is large enough that the motion is in an approximately straight line over the time considered. That means that the observer can be used to define a stationary (and inertial) frame of reference. The problem then reduces to a straight-forward one of kinematics (http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html). In a sense, the observer and projectile are both equally affected by the Earth's motion (as they are when they are together on the ground), so it washes out of the problem.

As for the specific problem given, the travel time for an object being thrown straight up in the air to a height of 100m above ground, then returning to Earth is about 9 seconds. And the difference in acceleration due to gravity over that distance is negligible (the distance travelled is tiny compared to the Earth's radius).

If the time/distance travelled and the required precision of the measurement is such that the Earth's motion must be taken into account, this can be dealt with by inclusion of the so-called Coriolis force and Centrifugal force. But if you're worried about those effects, you should probably also be modelling air resistance.

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