Beginner's questions on time dilation

[DarkMalice]

Hello,

I just started taking a Modern Physics course in University, and have a moderate understanding of time dilation. The problem is that I'm stuck with a problem I asked myself.

I understand the light clock thought experiment.

If you are within a rocket ship moving at a fast speed and a light pulse come from the floor vertically, hits the ceiling and returns to the floor, it take $$\Delta$$t= $$\frac{2h}{c}$$, where h is the height of the ship.

For someone observing from Earth, the light does not move in a straight line but in a triangle, and it would take instead $$\Delta$$t = ($$\frac{2h}{c}$$) / $$\sqrt{1-(v^2/c^2)}$$which is the time dilation formula.

My question was what would happen if the experiment was conducted on Earth? Within the reference frame of the Earth-dweller, $$\Delta$$t= $$\frac{2h}{c}$$, and inside the reference frame of the moving rocket, $$\Delta$$t =($$\frac{2h}{c}$$) / $$\sqrt{1-(v^2/c^2)}$$ Does this mean that now instead of time moving slower in the rocket, does it move faster? I know it can't just move faster just because I decided to do the experiment somewhere else, but I'm still confused.

 

[JesseM]

There is no frame-independent truth about which of two clocks is ticking "faster" or "slower" in relativity. If there is a light clock at rest on Earth and a light clock at rest on the rocket, then in the Earth's rest frame the rocket's light clock is running slower than the Earth's light clock, but in the rocket's rest frame the Earth's light clock is running slower than the rocket's light clock. To understand how this doesn't lead to any physical inconsistencies, you have to understand how time dilation goes together with length contraction and the relativity of simultaneity...take a look at the diagrams and explanation I gave in this thread if you're interested.

 

[timetravel_0]

Please understand that I am a enthusiast in theoretical physics and not an actual student or physicist. I simply like to understand the effects of physics in a practical way.

I always like to think of time as events. Time, as thought of by our minds, is a distorted effect. We think of time as ticks on a clock and that it moves in a linear way- however, time is actually just change(movement) in space. When change occurs, time occurs. A rock in space though not appearing to change is in fact always changing. Movement is change - and every object is always moving - hence change occurs. I like to call these changes events.

Now, I like to also think of everything that changes as 'broadcasters' of events. So, you are a broadcaster, I'm a broadcaster, the Earth is a broadcaster. Why use this term? Well, if I wave my hand in front of you, you see me wave it. If you wave your hand, I see you wave it. Simple enough, however, if the sun could randomly blinked its light off and on, we wouldn't see this event happen until 7 minutes later. Similarly, if you were in space at a distance of 1AU(the distance from the Earth to the sun) and you waved and I watched through a telescope, I wouldn't see you wave until 7 minutes later - hence why I call it broadcasting.

Now to the topic at hand, Time Dilation - there are two types of dilation - Gravitational and Speed. Dilation in relation to my broadcasting analogy can be thought of as a rate in which events occur. This events are broadcasted at the speed of light, however the amount of events that are observed are based on the dilation of time. In a gravitational field time is more dilated, so less events are broadcasted at the speed of light. In deep space, time is less dilated so more events are broadcasted at the speed of light. Now, speed(velocity) also dilates time - so the faster one moves the less events are broadcasted at the speed of light. Now, an observer can only measure the events with respect to his own rate. If two observers have the same rate of dilation, then the starting time for events(such as an exploding star) measured can be compared as equal. However, if one observer is at a higher rate of dilation than the other - then the starting time of the event will be different for both observers, as well as the length of time the event last will be different. However, regardless if the event is observed - the event still has is own rate of broadcasting.

Now, let's do a thought experiment - there are 4 probes in space, One near Earth with a high level of gravitational influence, another probe 1 light year away with less but some influence, and 2 probes another 2 light years away with little to no influence. Each probe will ping at the rate of 100 per YEAR. Now I will exaggerate a bit for simplicity - the probe near Earth broadcasts 1 event per light year, the probe 1 light year away will broadcast events at 2 per light year, and the two in deep space at 3 per light year.

So on earth, we could measure the probes pings in one years time. The probe near Earth will measure as 100 pings, the probe 1 light year away will measure 200 pings and the two in deep space will measure 300 pings. Now furthermore, the probes in deep space can measure each other as 100 pings in one year, then measure the pings from the probe in the middle to be 66 pings, and the probe on Earth as 33 pings. The probe in the middle in one year will measure Earth's as 50 pings, and the deep space probes as 150.

(Observed Probe Event Rate/Local Probe Event Rate) x Local Pings = Observed Pings.

Earth to Deep Space:
(3/1) x 100 = 300

Deep Space to Earth:
(1/3) x 100 = 33.3333

In a similar example using the rocket with using ticks on a watch rather than pings. Say the dilation of the rocket is .998 to Earth's 1 and your measuring 60 seconds.

Rocket to Earth:
(.998/1) x 60 = 59.88 seconds

Earth to Rocket:
(1/.998) x 60 = 60.12 seconds

The gravitational dilation will take effect as well as respect to being on Earth or in space. The speed dilation effect measured on Earth will be more noticeable than it will be if the rocket was in space. A rocket could theoretically go at as speed in a region of space to where the gravitational dilation is equaled to Earth's dilation by the speed of the rocket. What that means is - the rocket in space could have its time in sync with Earth under specific conditions. The only way for a rockets time to go faster than Earth's is if it were to be in a region of space where the gravity was more denser than Earth's and the speed dilation of the rocket doesn't overcome the gravitational dilation.

Feel free to comment and correct - As I said before, I am mearly an enthusiast in theoretical physics - these are some of the ideas I have been pondering over for awhile.