# Time dilation and speed of light

1. Aug 17, 2015

### DAC

Hello Physics Forum.
Given time runs slow as seen by a moving observer, why doesn't light travel further in the slowed time? Thereby negating the greater distance light has to travel, mirror to mirror in the light clock on the train thought experiment?

2. Aug 17, 2015

### Stephanus

Light always travel at the speed of light.

3. Aug 17, 2015

### Stephanus

Light ALWAYS travels at the speed of light. That is the short answer. But I'll try to give you a detailed answer. If this is not what you are asking then simply ignore it.

"Why doesn't light travel further in the slowed time". Light always travel at the speed of light.
There are two frames here.
1. Train frame
2. Platform frame.
According to the observer waiting on the platform -> platform frame is a rest frame, train frame is the moving frame.
According to the passenger on the train -> platform frame is a moving frame, train frame is the rest frame.

"Why doesn't light travel further in the slowed time with respect to (wrt) platform frame?". I think there are two objects in your question.
Light trajectory: Is the path the light takes wrt platform. Platform will see the light travels at 300,000 km/s. It cannot go further or shorter.
Time clock: Is the clock on the train that is seen by the platform: Platform will see the clock at the train slows down.
Perhaps you can answer this question, so you'll understand it.
Supposed there is a train. Its wide is 300 000 km. Or its wide is the distance light takes in 1 second. We'll call it its wide is 1.
The platform length is 450,000 km or 1.5
The train travels at 0.6c
When the train starts moving, a passenger in the train turns on his/her flash light toward a mirror at the other side of the car, 300,000 km away.
1. How much time does the train takes to reach the edge of the platform at 450,000 km away?
2. What is the light path as seen by the platform observer?
3. What is the light path as seen by the passenger?
So, you'll realize why "the light doesn't travel further at the slowed time"

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4. Aug 17, 2015

### DAC

Thanks but I asked why doesn't light travel further not faster.

5. Aug 17, 2015

### Stephanus

Okay, perhaps I don't understand your question.
Supposed this:
When the train starts to move a passenger in the train light its flash its torch.
After some time.
1. The clock on the platform shows (supposed) 500ms as seen by the observer on the platform
2. The clock on the train shows (supposed) 400 ms as seen by the observer on the platform
(for now, let's ignore why time in the train shows [EDIT: 400ms if the time on the platform shows 500ms]. The most important thing in this discussion is that the clock in the train shown slower then the clock on the platform)
3. The light from the torch light shown travels 150,000 km as seen by the observer on the platform
What do you mean the light doesn't travel further?
Why the light only travels 150,000 km as seen by the observer on the platform? Why not further?
It's been 4 hours since you post your question? Why PF Forum so quiet? Perhaps if there are some advisors take it over, both of us will get better answer.

Last edited: Aug 17, 2015
6. Aug 17, 2015

### Staff: Mentor

Travel further and greater distance are the same thing. It does travel further which is another way of saying it travels a greater distance.

I don't know how you think that those would negate each other since they are the same thing.

7. Aug 17, 2015

### Stephanus

I think the OP should state his/her answer more clearly.

Consider this scenario:

Speed: 0.6c; gamma = 1.25
Train car width: 300 meters
Train travels from point A to B then stop:
AB distance is 450 meters. wrt platform

-------------------------------------------------------------------------------------------------------------------------------
Time wrt platform = 2.5 micro seconds
Light path (hypotenuse) wrt platform: 375 * 2 = 750 meters
-------------------------------------------------------------------------------------------------------------------------------
AB distance is 360 meters. wrt train, is this relevant to the discussion?
Time wrt train = 2 micro seconds, for light to bounce back from the mirror at the other side of the car
Light path (train width) wrt train : 300 * 2 = 600 meters
-------------------------------------------------------------------------------------------------------------------------------

Why doesn't light travel further than 300 meters wrt train e.g 375 meters (wrt train) thereby negating the greater distance light has to travel?

8. Aug 19, 2015

### peety

The platform observer sees the light travel further, hence records a longer passage of time (given that the speed must remain c) than those on the train (who are aging more slowly).

9. Aug 19, 2015

### Stephanus

The platform observer sees the light travel further than whom?

10. Aug 19, 2015

### peety

Than those on the train. Put it like this, if a light is shone from one end of a train to the other then those on the train see it travel the length of the train. Those on the platform see it travel further and therefore record a longer passage of time. I'm sorry if this doesn't address your concerns, but it's the heart of SR.

11. Aug 19, 2015

### peety

My reply was for DAC and imagined the simplest possible thought experiment.

12. Aug 19, 2015

### Staff: Mentor

No, that's not correct. Time runs slow for a moving observer, as seen by a stationary observer. Think about how this distinction affects your reasoning.

13. Aug 19, 2015

### Stephanus

My concern? I just completed the OP question. The OP question does not complete.

14. Aug 19, 2015

### Stephanus

Now, it's all semantic here I think.
The platform sees the light travel farther than the passenger??
I can't imagine a scenario like that.
Imagine one spectator and two race car. A and B
The spectator sees car A travels farther than B.
Now, imagine two spectators (A and B) and one car.
A sees car travel farther than B. How can they reconcile this?
They somehow must develop a mean of communication. Even if they can develop a communication, their "now" are different by the time it takes light to travel from A to B.
And even if they can somehow communicate and calculate the time differences from the messages received, nobody can ever see the light travels from them.
We just can rely on the law of physics to "know" when we shine the light for 3 seconds "Ah, the light must have gone 900.000km" We just can't see the light.
All A and B can exchange is their clock reading.
Perhaps it will be easier if the question was modified to "Why the clock slowed down in the train as seen by the platform"
I think the answer "why doesn't the light travel further in the slowed time" is Light always travel at 300,000 km/s.

15. Aug 20, 2015

### peety

Can I stay with my simple experiment? The passenger sees the light travel exactly the length of the train and records, say, a millionth of a second. The platform sees the light travel the length of the train, plus the distance the train has moved. Because both agree the light travels at c, more time will have elapsed for the platform observer.
This may not be the scenario you're interested in, but I'm aiming for the utmost simplicity.

16. Aug 20, 2015

### Stephanus

Yes. I agree 100% with your points. As a matter of fact, I have already drawn the picture in post 2. But I'll upload it for you again.

Supposed, the width of the train is 300,000 km, we'll say that it's 1.
The length of the platform is 450,000 km, we'll say its 1.5. Half of the platform is 0.75
Train speed is 0.6c
The passenger sees light travel DF * 2 distance.
The platform sees the light travel AD * 2 distance.
What is AD distance? $AD = \sqrt{DF^2 + AF^2} = 1.25$
So in 1.25 sec wrt platform the train has traveled 0.75. 2.5 sec wrt platform, train = 1.5
So, 2.5 seconds wrt platform is 2 seconds wrt train.
It seems that you have understood SR (btw my SR is very weak ), so I don't have to tell you the diagram and the problem in detail.
DF length is 1.25. It conforms gamma factor $\gamma = \frac{1}{\sqrt{1-v^2}}$
Btw, where is the OP anyway?

17. Aug 20, 2015

### Stephanus

Come on DAC. Light travel "further" for the same given time is "faster", don't you think so?
But light travel "further" for a longer given time, then the speed might (might not) be the same. But, then, the clock in the train will match the clock on the platform won't it. And that's the entire point of debate between the two observer.
Clocks are not invariant
Light speed is invariant
Distances are not invariant

18. Aug 21, 2015

### peety

Very neat! It shows how useful Pythagoras was to Lorentz and Einstein.