# Time dialation

Discussion in 'Free Thoughts' started by Xelasnave.1947, Dec 2, 2017.

1. ### Xelasnave.1947Valued Senior Member

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I found in
http://ibphysicsstuff.wikidot.com/special-relativity...

The following.

Start
Derive the time dilation formula

If we do another “thought experiment,” this time with a light clock. If observer Y is on a train with a light clock traveling at a constant velocity, observer Y “sees” the light bounce back in forth in a vertical line. Whereas the observer on the ground sees the light bounce in a saw-tooth pattern as shown below. From this we can find a relationship between observer X’s time and observer Y’s time.

We can create a triangle of the motion. Where the hypotenuse is the distance traveled as seen by observer X, the light travels at speed c for time Δt. The vertical portion is the distance traveled as seen by observer Y. The horizontal portion is the horizontal distance traveled as seen by observer X. If we apply Pythagorean theorem:

End

In the second box where the observer is supposed to observe a passage of light following a saw tooth path I suggest is flawed.
It would seem that the light should, could only travel, at right angles to the little blue plate.
In other words in the moving box the light would move from point of origin and would not hit the second plate because the second plate has moved.
The light is not like a fly in a car... Or is it?
Does anyone see my point?
The light will leave at right angles to the plate and will hit a spot where the second plate was when the beam started off. So it would seem to me that there is no way in a travelling vehicle such as the thought experiment describes could have the observer seeing something that would not happen and further the observer in the train should see the same...as I said the light won't act like a fly in a car it must leave straight travelled straight and miss the other plate.
Does this have implications?
Alex

Last edited: Dec 2, 2017

3. ### Michael 345Next mythical choc bunnies for mystic who diedValued Senior Member

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I would contend it is like a fly

The problem I have is more with the speed of light, the hight of the carriage, length of mirrors

The WAY the diagram is presented, the sawtooth is so grossly out of scale it really does not do justice to the concept

I think the concept is sound but impossible to draw to scale

5. ### Michael 345Next mythical choc bunnies for mystic who diedValued Senior Member

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The dashes are light beam photons

Last edited: Dec 2, 2017

7. ### Janus58Valued Senior Member

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The point is that light does not behave either like you are describing in your last paragraph, nor exactly like a fly in the car.

In your last paragraph, you treat light as if it moves relative to some fixed reference frame which everyone agrees on (in this case, that of the road). Thus in this view, if the box is moving relative to this reference frame then the light shot at a right angle to the motion of the box would miss the mirror, and the light seem to travel at an angle relative to the boxand at a right angle to the road according to everyone.
With the Fly model (or better yet a ball bouncing back and forth between the two blue plates), The ball travels up and down relative to the box, always hitting the plates. In this view the ball follows a zig-zag pattern relative to the road. Everyone will agree to this.
Now in both these models, if the the speed of the light is measured as c in the frame in which the light is going up and down, then the speed of the light relative to the frame in which it appears to travel in a zig-zag would be sqrt(v^2+c^2), if v is the speed of the box. This gives an answer of more than c.

However, neither of the above works for light. It turns out that there is no way for the person in the box to tell if he is moving or not. He starts the experiment with the light bouncing back and forth between the mirrors. He then changes his speed and repeats the experiment. The light still bounces up and down between the mirrors. Now matter how much he changes his velocity between performing the test, the light always bounces back and forth between the mirrors. In this way, it is similar to the ball bouncing back and forth.

Where this deviates from the earlier ball model is how a person standing the road measures what is happening. Like in the ball model, the light will travel a zig-zag pattern relative to him. But unlike the ball model, it will still only travel at c relative to himself and the road, not faster than c.

If we assume that he has his own light bouncing back and forth between two mirrors and that his set of mirrors is aligned with the other set when they start, then things will look like this to him:

The numbers represent time measured on clocks affixed to both sets of mirrors. You will note that the clock for the moving set runs 1/2 as fast. This is because, according to someone traveling with this set of mirrors, the light is traveling at c relative to the mirrors and only take 1 time unit to make the round trip. In fact, if we were to look at this animation from the reference frame of the mirrors moving the right, seeing them as standing still while the other set of the mirrors are moving to the left, then it would be the other clock that would be ticking 1/2 as fast. (keep in mind, that we haven't physically changed anything here, we have just switched which reference frame we are measuring from.)

Now it is important to not put too much importance to light here. It isn't the behavior of light that is "causing" this effect, rather that the behavior of light is revealing something fundamental about the very nature of time and space. Even if we replaced the light with a bouncing ball, we would get the same result in terms of how fast each system would view the other ball as bouncing. This is because the simple ball model we used above is not correct according to the rules by which our universe works and the velocity of the ball along the diagonal will not be found by the simple equation I gave above, but a more complex one.

The whole point is that the universe doesn't behave by either of the simple models I started with, but in a third way. The only reason we assumed that these other models were correct is that the difference between the answers arrived at with these models differed so slightly from the correct answer when working with velocities that are small compared to c (which until not too recently were the only examples we had to work from), that we just didn't see it. Also, the first two models just seem more intuitive.

As non-intuitive as the Relativistic model of the universe may seem, modern observation and experiment has shown it to be the most correct one. In essence, you were basing your argument on how you thought light "should" behave rather than on how it does.

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Yes I agree.
Alex

9. ### Xelasnave.1947Valued Senior Member

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For the record I don't understand SR well enough to have a problem with the theory.

I did think the thought experiment was flawed however but I have learnt long ago not to argue against a proposition or scientific theory by picking flaws in the example or any mind experiment used to conceptualise the matter.
It is 4-50 am and I only got out of bed to get a drink of milk so it will be better to review your post later.
I did think I would take the time to thank you.
Alex

10. ### SeattleValued Senior Member

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2,763
The light does hit the plate at right angle for the observer in the train car. It can't for the observer on the platform due to movement. Since the speed of light is fixed and it's traveling further in the second box, time is the only other thing that can give.

When you are in an airplane, reading a book, the light above your head doesn't end up in the seat behind you even though you are traveling at 400 mph (or whatever speed). It seems as if you aren't moving while you are reading that book and yet you have traveled potentially hundreds of miles while reading it.

On the ground someone would be well aware of your movement.

11. ### Xelasnave.1947Valued Senior Member

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Thanks for you input.
I have only now, 8-30 am, awoke but off the top of my head I don't see it the way you do.
I will think about it more but why would the light move?
Why should it not travel at right angle to the ground.
Perhaps you can tell me why and I suggest the anology of sitting in a plane is of no help as any deviation would not be noticed.
The light travels about six feet at approx 300,000 klms per second so measured against the speed of the plan even if at c its not very much.
The formula tells us the answer but if the light travels at right angles all could only observe the light travelling up and backwards in my view.
I suggest the only way to determine what happens is to do an actual experiment and take it out of the realm of speculation.
Well that would be hard as there would be only a split second for the outside observer to glimpse anything inside even if the box was travelling slow...try looking in a car window as it passes..very little time ..you could only get a snap shot..the sums would tell us that I am sure.

But I can not see why light would chase after the other plate as in the little diagram.
To suggest it acts like a bouncing ball, or follow a similar path is where I find difficulty and say I can't see that it would and I bet experiment would support that opinion.
Anyways enough talking off the top of my head I best think about all the answers given.
Alex

Last edited: Dec 2, 2017
12. ### Xelasnave.1947Valued Senior Member

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Please be patient with me but I say he must see the light bending towards the rear of the box.
Why would the light behave like a bouncing ball is my difficulty.
I need to think that thru.
I would have thought light will travel in a straight path unrelated to frame irrespective of observation.
Let me think more about it.
Thanks again.
Alex

13. ### Xelasnave.1947Valued Senior Member

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I understand that is the result but it will not apply if the light travels straight..
If anything would not the outside observer observe the light bending towards the back of the box..in which case the formula could still be applied.
I must go but I will read your post a few more times in the hope of seeing how SR sees it.
Alex

14. ### SeattleValued Senior Member

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Forget the thought experiment then. The speed of light has been measured. We now know that it is a constant.

Therefore, if it travels the same speed when you are at rest as when you are moving very fast what has to give is time. Time has to slow down as speed increase otherwise you end up with light going faster than C.

15. ### Xelasnave.1947Valued Senior Member

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Well it must ...the mind experiment shows it does.

No my post is only about it...I am not railing against SR only my belief the thought experiment is flawed.
Alex

16. ### Xelasnave.1947Valued Senior Member

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Could we substitute the box with a flat bed vehicle with a lazer pointing straight up at right angles to the ground and the floor of the vehicle.
Let the vehicle pass by at a fair speed and fire the beam ..what would each observer observe?
Alex

17. ### DaveC426913Valued Senior Member

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Look at the angle of the first beam. It has been emitted at a 45 degree angle.

It travels to the second mirror in a straight line (45 degrees to the breadth of the plane), and then reflects off a flat mirror. Since its incident ray is 45, its reflected ray is also 45, and it continues on its way.

So the only question is: why did the light ray get emitted at an angle in the first place?

Why must it be emitted at a right angle?

Consider the source of the light. A laser or a flashlight. Consider the light ray passing down the length of the laser or out of the flashlight's bulb. From the stationary person's perspective, the path of light beam emission is a 45 degree angle.

18. ### SeattleValued Senior Member

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The same thing as in the thought experiment.

19. ### DaveC426913Valued Senior Member

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During the time the light traveled the length of the laser's pumping chamber, the chamber has been moving (to the right, in the original experiment). So the light particles have been following a 45 degree path (from the stationary observer's perspective) even before they exited the laser.

You would not expect light to exit the laser's chamber and immediately make a 45 degree turn so as to move vertically. It continues on the same path it had when it was inside the laser - which is moving.

20. ### Xelasnave.1947Valued Senior Member

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Thanks for contributing Dave.
Yes I noticed.
That works for me assuming one arrived at that angle so as to hit the plate..like leading the target in a skeet shoot.
Alex

21. ### Xelasnave.1947Valued Senior Member

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Fired at right angles?
Alex

22. ### Janus58Valued Senior Member

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The thought experiment could only be flawed if SR were wrong, as it is entirely built on how SR says light would behave under these circumstances.

Imagine that it is the box that is "stationary" and the outside observer that is moving. Wouldn't you expect the light to travel from blue line to blue line in the box? The outside observer would then see the light travel in a zig-zag path relative to himself. ( if the light hits a given spot on the opposite wall according to the observer in the box, the light must hit that same spot on the wall of the box according to the outside observer.)
Now neither observer can tell which of the two of them is "really" moving (in fact, it is meaningless to talk about anything than the relative motion between the two observers) Either observer sees exactly the same thing whether he considers himself as moving or the other observer as moving. So if the outside observer sees the light travel back and forth between the mirrors in the box if he is moving past a "stationary" box, he sees the same thing if he is "stationary" and the box moves past him.

23. ### DaveC426913Valued Senior Member

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At right angles, but moving.