time dilation confusion

[earthlight]

I'm confused about time dilation. I thought it meant the speed a clock ticks as a function of the speed the clock is moving. Lets say a clock is on an object A that is approaching object B. Lets say someone on Object B shines a light on object A. There will be time dilation due to the speed of object A that will make the speed of light appear to be constant no matter how fast B approaches A. We can describe that as deltaTA/deltaTB. That describes the speed at which the clock is ticking. Lets say someone on object fires an object at 10 miles an hour toward object A. Why doesn't a person on object A measure the speed of the approaching object as 10 * deltaTB/deltaTA. Shouldn't the speed of the clock affect all speed measurements and not just the measurement of the speed of light.

[swansont]

Time dilation happens to objects that are moving, according to you, who is always at rest. (if motion is inertial, i.e. no accelerations)

 

If an observer is on A, his/her time runs normally. The dilation occurs on the object moving toward them

[md65536]

Lets say someone on object fires an object at 10 miles an hour toward object A. Why doesn't a person on object A measure the speed of the approaching object as 10 * deltaTB/deltaTA. Shouldn't the speed of the clock affect all speed measurements and not just the measurement of the speed of light.

deltaTB/deltaTA would be the inverse of the Lorentz factor, which isn't equal to velocity.

 

All speed measurements are similarly affected in that if a moving object B fires another object towards the observer, then the velocity of the projectile relative to A can be calculated using the "composition of velocities" formula. The formula works for all values up to and including c. If you consider a photon as a projectile and use c in that formula, the result is that both A and B calculate the relative speed of the photon is c.

[earthlight]

Swanson, the person who is measuring the speed is on object A. Isn't it his time that matters in the velocity calculation.

md65536 let me rephrase the question this way. Supposing there are two stationary objects A and D and object B is moving toward D and a light is being shown from A on B and from D on B. The clocks on A and D are moving at the same speed. Lets say the clock on B is moving slower than on D. That means the clock on B is moving slower than on A since the clocks on A and D are the same. If that were the case though you would measure one of the light beams as going faster than the speed of light.

[swansont]

Swanson, the person who is measuring the speed is on object A. Isn't it his time that matters in the velocity calculation.

Yes. And A's time runs normally, according to A, since A is not moving with respect to A.

[Janus]

Swanson, the person who is measuring the speed is on object A. Isn't it his time that matters in the velocity calculation.

md65536 let me rephrase the question this way. Supposing there are two stationary objects A and D and object B is moving toward D and a light is being shown from A on B and from D on B. The clocks on A and D are moving at the same speed. Lets say the clock on B is moving slower than on D. That means the clock on B is moving slower than on A since the clocks on A and D are the same. If that were the case though you would measure one of the light beams as going faster than the speed of light.

 

As far as B is concerned, he is not moving, A and D are. Also, time dilation is not the only effect to consider. There is also length contraction and the Relativity of simultaneity.

 

As far as A and D are concerned, B. clock runs slow. Which is why it shows less time for the trip than what the clocks at A and D does.

 

As far as B is concerned, his clock runs at normal speed, but the distance between A and D is shorter than it is as as measured by A or D, Thus the trip takes less time.

 

Relativity of simultaneity comes in when any of the above deal with clocks that are separated from each other along the line of motion and are moving with respect to the observer.

 

So for example, if B had clocks at the front and back of his ship that were synchronized according to B, then according to A or D, the clock in the front would read behind the clock in the rear.

 

As far as B was concerned, the clock at D would read ahead of the clock at A.

 

So if I'm at A or D, according to me, the time it takes for light coming from D to travel from front to back of B is less than that for the Light coming from A to travel from back to front. But, since at the moment the light hits the front clock, the rear clock already reads a later time, By the time the light reaches the rear clock, it will read even later.

 

Conversely for light coming from A, when it hits the back of B, the clock at the front reads earlier, So when the light reaches it, it won't read quite as late.

 

The upshot is that if the the light from A hits the back of the Ship when that clock reads 0 sec and hits the front clock when it reads 1 microsecond, then the light coming from D that hits the front clock when it reads 0 sec, will hit the rear clock when it reads 1 microsecond.

 

For B, the same 1 micro second difference in clock readings occur, however according to him, the clocks at the ends of the ship are in sync, so the light actually takes 1 microsecond to cross the ship in both directions and thus travels the same speed in both directions.

[md65536]

md65536 let me rephrase the question this way. Supposing there are two stationary objects A and D and object B is moving toward D and a light is being shown from A on B and from D on B. The clocks on A and D are moving at the same speed. Lets say the clock on B is moving slower than on D. That means the clock on B is moving slower than on A since the clocks on A and D are the same. If that were the case though you would measure one of the light beams as going faster than the speed of light.

I don't see how the last statement follows, unless you assume that relative velocities add like they do in Galilean relativity. See http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_theory_of_relativity and note that if you use a value of c for either u or v, the end result is c. In other words, whatever the speed of the source of light, the speed of photons projected from it will still be c. The reason why this works is that the composition formula is derived from consistent equations that begin with the assumption that the speed of light is c regardless of the source. Better understanding might come from looking at how it is derived?

 

It might help to know that the invariance of c isn't a prediction of SR, but an assumption of it. Based on experimental evidence, it was observed that the speed of light is c regardless of the motion of its source, in all measurements ever made and in all experiments. The equations of SR are a description of how that can be possible and be consistent, and of how other things like time and distance must then relate.