Is my thought right or wrong? Light and a moving observer

In summary, the conversation discusses the concept of time dilation through the example of a standing person and a car moving at different velocities. It highlights the importance of specifying frames when giving positions, velocities, and times in relativity. The conversation also mentions the common error of switching frames implicitly without noticing. It concludes that all questions about time dilation are frame dependent.
  • #1
thatoekhant
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I would like to know whether my thought is right or wrong about time dilation example.

Let's say,

A person is standing at a starting point so his velocity is 0 ms'1.
A car runs from that point in the velocity of 3 ms'1.
A photon from a light source at that point is also emitted at the same time. Let the velocity of photon be 5ms'1.( Yeah I know the real velocity of photon)

Relative velocity of the photon is 5ms'1 for both standing person and car.

For the standing person at the starting point, the photon is at 50 meters ahead of that point after 10 seconds.
For the car, the photon is at 50 meters ahead of it after 10 seconds. At that time, the car is at 30 meters ahead of the starting point and so the photon is at 80 meters from that point.

That means, for the standing person, it takes 16 seconds to find the photon reach 80 meters away from the standing point. Yet, for the car, it takes just 10 seconds to find the photon reach 80 meters away from that point. When the person looks at the clock of the car, the clock motion of the car is running slower than his.
 
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  • #2
You can make the problem a bit easier by stating the distances on light-seconds instead of meters: the speed of light is one light-second per second.
 
  • #3
thatoekhant said:
A person is standing at a starting point so his velocity is 0 ms'1.

His velocity in the frame in which the starting point is at rest is 0. When you give positions, velocities, and times, you need to specify a frame; otherwise they are meaningless. One of the most common errors in relativity is to fail to do that, and then not notice that you are switching frames implicitly. As you will see, you yourself have made that mistake.

thatoekhant said:
A car runs from that point in the velocity of 3 ms'1.

Velocity in the frame in which the starting point is at rest.

thatoekhant said:
A photon from a light source at that point is also emitted at the same time. Let the velocity of photon be 5ms'1.

Or just 5, without units. That way you don't have to pretend the speed of light is something other than it is.

Or we could just make the photon's velocity 1 and the car's velocity 3/5. (Units in which the speed of light is 1 are very common and useful in relativity.)

thatoekhant said:
Relative velocity of the photon is 5ms'1 for both standing person and car.

Yes (with the caveat I gave above about velocity units). But these velocities are expressed in different frames--one in the rest frame of the starting point, one in the rest frame of the car.

thatoekhant said:
For the standing person at the starting point, the photon is at 50 meters ahead of that point after 10 seconds.

In the frame in which the starting point is at rest.

thatoekhant said:
For the car, the photon is at 50 meters ahead of it after 10 seconds.

In the frame in which the car is at rest.

thatoekhant said:
At that time, the car is at 30 meters ahead of the starting point and so the photon is at 80 meters from that point.

No. You just switched frames implicitly (between the two sentences quoted just above) and didn't notice it, which is the error I said above was very common. Can you see how?

(If you can't, consider the following questions: In what frame is the car 30 meters ahead of the starting point in 10 seconds? In what frame is the photon 50 meters ahead of the car in 10 seconds? Hint: they are not the same frame. So you can't add the distances, because you're adding distances relative to different frames, which is meaningless.)

thatoekhant said:
That means, for the standing person, it takes 16 seconds to find the photon reach 80 meters away from the standing point.

In the frame in which the starting point is at rest, yes.

thatoekhant said:
Yet, for the car, it takes just 10 seconds to find the photon reach 80 meters away from that point.

No. See above.
 
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  • #4
Then, how many meters away from the starting point will the photon be after 10 seconds in the car's clock, Sir ? not 80 meters ?
 
  • #5
thatoekhant said:
Then, how many meters away from the starting point will the photon be after 10 seconds in the car's clock, Sir ? not 80 meters ?
How are you defining the start point? Is there a marker there? Is that marker at rest with respect to the ground or the car?
 
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  • #6
thatoekhant said:
how many meters away from the starting point will the photon be after 10 seconds in the car's clock, Sir ?

In which frame? The car's frame?
 
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  • #7
thatoekhant said:
Then, how many meters away from the starting point will the photon be after 10 seconds in the car's clock, Sir ? not 80 meters ?
Yes, 80m, in the car's frame of reference. The kinematics are relatively simple.

To the person at the starting point, the car is moving away at 3m/s and the light at 5m/s.

To the person in the car, the light is moving at 5m/s ahead and the starting point is moving at 3m/s behind him.

Both can carry out normal kinematic calculations on that basis.
 
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  • #8
PeterDonis said:
In which frame? The car's frame?

Yes, Sir, Then am I right ?
 
  • #9
PeroK said:
Yes, 80m, in the car's frame of reference. The kinematics are relatively simple.

To the person at the starting point, the car is moving away at 3m/s and the light at 5m/s.

To the person in the car, the light is moving at 5m/s ahead and the starting point is moving at 3m/s behind him.

Both can carry out normal kinematic calculations on that basis.

Then, doesn't it mean the clock of the standing person ticks 16 times when that of the car ticks 10 times, Sir ?
 
  • #10
thatoekhant said:
Then, doesn't it mean the clock of the standing person ticks 16 times when the that of the car ticks 10 times, Sir ?
All such questions are frame dependent. In the frame of the person at the start the car clock ticks slower. But, in the car frame tge starting clock runs slower.
 
  • #11
thatoekhant said:
Then, doesn't it mean the clock of the standing person ticks 16 times when that of the car ticks 10 times, Sir ?
Unfortunately, simultaneity is also frame dependent. So what's happening at the same time as the car clock ticking 10 depends on which frame you use, because they have different definitions of "at the same time" for things that don't also happen in the same place.
 
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  • #12
Ibix said:
Unfortunately, simultaneity is also frame dependent. So what's happening at the same time as the car clock ticking 10 depends on which frame you use, because they have different definitions of "at the same time" for things that don't also happen in the same place.

Sir, what I would like to know in my layman sense is whether the clock of standing person ticks 16 times when the clock of car ticks 10 times or not. That's why in the frame of standing person, the clock of car is running slow.
 
  • #13
PeroK said:
All such questions are frame dependent. In the frame of the person at the start the car clock ticks slower. But, in the car frame tge starting clock runs slower.

I understand " In the frame of the person at the start the car clock ticks slower"

But, I don't understand " But, in the car frame tge starting clock runs slower" , should it have not been faster, sir ?
 
  • #14
thatoekhant said:
I understand " In the frame of the person at the start the car clock ticks slower"

But, I don't understand " But, in the car frame tge starting clock runs slower" , should it have not been faster, sir ?

The basic description of time dilation is that moving clocks tick more slowly. But motion is relative, so no clock can be said to be absolutely moving. If I'm in a ship flying away from you at some speed, for you, my clock is ticking more slowly. But for me, you're the one who's moving, so your clock is ticking more slowly. This may seem contradictory until you incorporate the relativity of simultaneity. At some given moment X for you, my clock says Y. But for me, when my clock says Y, your clock says Z. We don't share the same concept of "now" due to being in motion relative to each other.
 
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  • #15
PeroK said:
To the person in the car, the light is moving at 5m/s ahead and the starting point is moving at 3m/s behind him.

Ah, yes, you're right.

However, that still doesn't quite address the question about time dilation. I'll address that in response to @thatoekhant below.

thatoekhant said:
Then I am right ?

You are right about the 80m in the car's frame, yes; I was mistaken about that. However, that still doesn't mean you can make the comparison you make here:

thatoekhant said:
for the standing person, it takes 16 seconds to find the photon reach 80 meters away from the standing point. Yet, for the car, it takes just 10 seconds to find the photon reach 80 meters away from that point. When the person looks at the clock of the car, the clock motion of the car is running slower than his.

To really understand what's going on, you need to first label all the events of interest in one frame (say the frame in which the starting point is at rest) and give them their proper coordinates in that frame. That means you need to identify what those events are. For example, there is an event at which the photon is 80 meters from the starting point in the rest frame of the starting point. There is also an event at which the photon is 80 meters from the starting point in the rest frame of the car. Question: are these the same event? (Hint: the answer is no. There are two separate events, each of which has its own distinct coordinates. So the comparison you make in the quote above is still comparing quantities that can't be directly compared.)

Once you have coordinates for all events of interest in one frame, you then Lorentz transform all of those coordinates into the other frame (the frame in which the car is at rest). That tells you how things look from the car's point of view.

Once you have described things in both frames, you can then look at what "time dilation" means in each frame. In the starting point rest frame, the car's clock appears to run slow; but in the car rest frame, the starting point's clock appears to run slow. That means the two comparisons must be comparing different things (similar to the way there were two events involving the photon above, not one). What are those different things?
 
  • #16
thatoekhant said:
should it have not been faster, sir ?

No. Do the math as I described in my previous post and see.
 
  • #17
thatoekhant said:
Sir, what I would like to know in my layman sense is whether the clock of standing person ticks 16 times when the clock of car ticks 10 times or not. That's why in the frame of standing person, the clock of car is running slow.
There isn't a consistent answer in these terms. A major consequence of relativity is that time doesn't work the way we naively think about it.

Both observers regard the other's clock as ticking slowly. This might appear inconsistent, but that's because youare thinking of "at the same time" as an absolute statement. It's not. It's like saying "straight in front of me". What that statement means depends on which way I'm facing, and means something different when soneone else says it. In relativity, "at the same time" turns out to depend on who says it and their state of motion. So "what happens at the same time as the car clock ticks 10?" can only be answered if you decide whose "same time" you mean.

If you use the car's definition of "the same time" then the ground clock shows 8.125s when the car clock reads 10. If you use the ground's definition of "the same time" then the ground clock reads 12.5s when the car clock reads 10s.

Note that we are correcting for light travel time here. If we don't correct for that, both frames will agree what time the car observer sees on the ground clock, so there is no contradiction inactual measurements. They also agree that what they see is not what's happening "now" because of the finite speed of light. But they don't agree on how to correct for the speed of light because they don't agree what "not moving" means, so they can't agree what "now" means.

Einstein's train thought experiment is the usual illustration of this.
 
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  • #18
Ibix said:
In relativity, "at the same time" turns out to depend on who says it and their state of motion. So "what happens at the same time as the car clock ticks 10?" can only be answered if you decide whose "same time" you mean.

If you use the car's definition of "the same time" then the ground clock shows 8.125s when the car clock reads 10. If you use the ground's definition of "the same time" then the ground clock reads 12.5s when the car clock reads 10s.

Yeah, I think I understand what that means, Sir.
 
  • #20
thatoekhant said:
Sir, what I would like to know in my layman sense is whether the clock of standing person ticks 16 times when the clock of car ticks 10 times or not.

Let's say the 16-tick period of time starts at the same time as the 10-tick period of the other clock. The only way we can establish that as an absolute fact is if the clocks share the same location. It's tempting now to say that the 16-tick period ends at the same time as the 10-tick period, but no such claim can be made absolutely because the clocks are in same place only that one time.
 
  • #21
Arkalius said:
But motion is relative, so no clock can be said to be absolutely moving.
An accelerating clock is absolutely moving.
 
  • #22
David Lewis said:
An accelerating clock is absolutely moving.
Yeah, what he said.
 
  • #23
David Lewis said:
Arkalius said:
But motion is relative, so no clock can be said to be absolutely moving.
An accelerating clock is absolutely moving.
In relativity, the concept of "absolute motion" doesn't exist, so it is meaningless to say that something is "absolutely moving".
 
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  • #24
David Lewis said:
An accelerating clock is absolutely moving.
That statement is not exactly incorrect, but it is unclear enough to be interpreted in several different ways, some of which are incorrect.

Proper acceleration is absolute (in the sense that that the word is being used in this thread), coordinate acceleration is not, and there exists no inertial frame in which an object undergoing proper acceleration can be more than momentarily at rest.
 
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  • #25
DrGreg said:
In relativity, the concept of "absolute motion" doesn't exist, so it is meaningless to say that something is "absolutely moving".
I'm swinging a rock around on a string, so either the whole universe is spinning, or my rock is moving.
 
  • #26
David Lewis said:
either the whole universe is spinning, or my rock is moving.

Yes. And according to GR, both viewpoints are valid.
 
  • #27
David Lewis said:
I'm swinging a rock around on a string, so either the whole universe is spinning, or my rock is moving.
At any given instant, it may be taken to be moving or not as one pleases. There is no inertial frame in which it is continuously at rest. But that's not the same thing as saying that it is always moving.
 
  • #28
About the OP, I got a shortcut answer.

Let's get practical! The speed of light one way is impossible to measure, and the OP assumes that it is. In real life, we will never have to solve that kind of problem, because we will never face it, so it is no use to study it.
 

1. Is light affected by the motion of the observer?

Yes, according to the theory of relativity, the speed of light is constant and independent of the motion of the observer. This means that the speed of light will always be the same, regardless of whether the observer is stationary or moving.

2. Can a moving observer perceive light differently?

No, the perception of light is not affected by the motion of the observer. The speed of light remains constant for all observers, regardless of their relative motion.

3. Does the movement of the observer affect the wavelength of light?

No, the wavelength of light is also constant and independent of the motion of the observer. This means that the color or frequency of light will not change for a moving observer.

4. How does the theory of relativity explain the behavior of light for a moving observer?

The theory of relativity states that the laws of physics, including the speed of light, are the same for all observers in uniform motion. This means that a moving observer will perceive light in the same way as a stationary observer.

5. Can a moving observer measure the speed of light differently?

No, the speed of light is always measured to be the same value, regardless of the observer's motion. This is a fundamental principle of the theory of relativity and has been confirmed through numerous experiments and observations.

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