Time Dilation - Albert Einstein and the Theory of Relativity

Two spaceships are traveling together through the galaxy at close to the speed of light. Mounted on one ship is a laser that can fire pulses of light, and on the other, a mirror. The pilot of the first ship fires a pulse at the mirror, and watches as it is reflected back. A clock on board measures how long the round trip takes.

But now suppose that he does this as the ships are passing an observer on a nearby asteroid. According to relativity theory, this observer sees the pulse moving through space at exactly the same speed that the pilot does -- namely, the speed of light. But he also sees the pulse traveling a longer distance, because from his perspective, he must add the forward motion of the ships to the motion of the pulse between them. So he measures a longer time interval for the round trip than the pilot does, because he is watching the pulse go farther without going any faster. This effect is called time dilation: if one observer is moving with respect to another, each perceives that the other's time is flowing more slowly.

National Science Foundation

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[Fetcher23]

The definition of respect is "in relation to something". Forget the asteroid. If only the 2 ships were out there, their movement or non movement is in respect to the other, one pilot could say "in respect to that other ship we are not moving". If one ship slows down a touch, each ship observes the difference in respect to the other. If only the 2 ships were out there (same speed) they would not perceive the others time flowing more slowly which is why I said the statement is wrong.

[Crimson REd]

thank you ;)

[xXRainKingXx]

Nature is quite amazing.

[LeconsdAnalyse]

2/2

The asteroid observer also sees the ships (moving together in the x direction with speed v) move a distance vt in time t according to his/her timer. Both timers are initially synchronized and working ideally.

Therefore, using the invariant interval of the light pulse:

c²t`²- L² = c²t²- L²- v²t² OR, c²t`² = c²t² - v²t² OR, c²t`² = (c² - v²)t² OR, c²t`² = c²(1 - v²/c²)t² OR, γt` = t.

[LeconsdAnalyse]

1/2

The situation in the clip is taking place in 2+1 (i.e., ℝ²⁺¹).

Relative to the pilot the light travels path L (the REST distance between light source and mirror) in the (say) y direction (of an xy plane) in time t` according to his/her timer.

[METELUANA]

this is why the lorentz transformation equation is linked to the e=mc^2 equation. The vectors relativistic mass and the speed of light are related there too though for use in measuring electronvolts in accelerators.

[Jason92881]

Think about when your 20,000 feet up in the air on a 747 going 400 miles per hour and you look down on a city. The cars and people below seem to be moving slower and more in harmony with each others movement. From the ground a person looking at the 747 might feel the plane is moving rather slowly not 400mph or however fast 747's move

[PeaceandLove754]

Interesting.

[surgerguy322001]

Hmmmm. Actually I must think more about the trails of light. So I will retract what I said before about them, .... since no matter the speed of the ship as long as it is at a constant velocity and not c, each observer will see light travel at c. For now just think of the trails in aiding the direction of the laser pulse.

Now, Time dilation happens only in the direction of travel. for the brief moment it's passing you, you are watching the light travel in a v shape parallel to the ship.

[Adyugupta]

Thanks for the clarification! :-)

[I'm shenoku]

I'm sorry, I'm having trouble understanding your comment. Can you elaborate? You can even direct message me if the explanation is lengthy. And how does the film actually slow down the ships and how does that force light to have length?