Which Watch Will Have Slower Time: Object 1 or Object 2?

[Sandip Patel]

Assumption: Object 1 is moving and object 2 is static.
It is impossible to say which object is moving without any reference object 3. There are three scenarios possible.
1. Reference object 3 is at same position in space time with object 2, then object 1 is moving and object 2 is static.
2. Reference object 3 is at same position in space time with object 1, then object 2 is moving and object 1 is static.
3. Reference object 3 is at different position in space time with object 1 and object 2, then both objects are moving.

Assume that object 1 and object 2 have watches.

According to Einstein's theory, time slows down for the moving object than the static object.

Question: If object 1 is moving at the speed of light at some speed large enough that time dilation effects are noticeable, which watch will have slower time? Watch with object 1 or watch with object 2?

 

[phinds]

Question: If object 1 is moving at the speed of light ...

Since this is impossible, any question which follows is meaningless.

 

[Sandip Patel]

Since this is impossible, any question which follows is meaningless.

Dear Phinds, I was trying to understand which object will see the difference in watch. Time of object 1 and object 2 are absolute that are readable at any space time. Now if time dilatation happen, which watch will have slowed down time. Please help me understand the practical result if we have such case.

 

[Nugatory]

Dear Phinds, I was trying to understand which object will see the difference in watch...

@phinds is (correctly) saying that your question cannot be answered because it has no correct answer. The problem is that you have specified that "object 1 is moving at the speed of light"; but time dilation, like all of relativity, requires that nothing can move at the speed of light. Thus, your question is like asking "If $a$ and $b$ are integers and $(a/b)^2=2$ then what is the sum of $a$ and $b$?" - there is no right answer.

However, we can save your question by changing it to,"object 1 is moving at some speed close to the speed of light" and now we have a physically reasonable situation and we can talk about how time dilation will work in that situation. I've made the correction in the original post because it seems from your follow up that that's what you meant. Let me know if it is not.

 

[Nugatory]

This thread was temporarily closed, is now open again.

 

[mfb]

Time of object 1 and object 2 are absolute that are readable at any space time.

Different observers will disagree on what "at the same time" means. Relativity of simultaneity is a key aspect of special relativity. For speeds close to the speed of light but below (has to be below): Both observers will measure the clock of the other one go slower.

 

[Nugatory]

Both observers will measure the clock of the other one go slower.

And in the third case (both clocks are moving relative to the reference object): an observer at rest relative to the reference object will find both clocks to be slower than his own. If their speeds relative to the reference object are not the same, the clock with the faster-moving object will tick more slowly than the clock on the slope-moving object.

 

[sweet springs]

It is impossible to say which object is moving without any reference object 3.

Movement is relative between 1 and 2. 1 is moving for 2. 2 is moving for 1. 3 has nothing to do with this relative motion between 1 and 2.

We say velocity of obeject a in IFR where object b is still $V_{ab}$,
$$V_{12}=-V_{21},V_{23}=-V_{32},V_{31}=-V_{13}$$

In a's IFR, b clock tick slow by factor $f(V_{ba})$ and c clock ticks slow by factor $f(V_{ca})$.
where {a,b,c}={1,2,3} and $f(V)=\sqrt{1-\frac{V^2}{c^2}}\ <\ 1$. For everybody his/her clock ticks fastest.

 

[LURCH]

For everybody his/her clock ticks fastest.

And this remains true whether the two clocks are moving toward or away from one another, correct? (So long as their speed relative to one another is the same, of course.)

 

[Ibix]

And this remains true whether the two clocks are moving toward or away from one another, correct?

Yes. Note that you will actually see clocks coming towards you ticking faster and those going away ticking slower, due to the Doppler effect. Once you correct for the distance change, what is left over depends solely on relative speed.

(So long as their speed relative to one another is the same, of course.)

Not sure I understand this. If your velocity relative to me is v, my velocity relative to you is -v, always.

 

[m4r35n357]

dilatation

Incidentally, the correct word is "dilation".

 

[FactChecker]

Assumption: Object 1 is moving and object 2 is static.
It is impossible to say which object is moving without any reference object 3.

Even then it is not possible, since you can legitimately hypothesize that two (or even all) objects are moving. You are missing the critical idea. No matter which object you consider to be "stationary", special relativity describes how the "stationary" observer would see the other objects behave. And the "stationary" observer can use special relativity to understand how there is a disagreement between his observations and the observations of the other objects when they assume that they are the "stationary" ones. So it makes all the observations logically consistant, no matter which one (or many) assumes that he is "stationary".

 

[Dale]

Question: If object 1 is moving at the speed of light at some speed large enough that time dilation effects are noticeable, which watch will have slower time? Watch with object 1 or watch with object 2?

The question needs a little more information about the reference frame in question. Clearly it is a reference frame where object 1 is moving, but you have provided no information about the speed of object 2 in this frame. So we cannot determine which one will be more or less time dilated in this frame.

 

[Sandip Patel]

The question needs a little more information about the reference frame in question. Clearly it is a reference frame where object 1 is moving, but you have provided no information about the speed of object 2 in this frame. So we cannot determine which one will be more or less time dilated in this frame.

Thanks Dale! Here I am modifying the question for better understanding.

Assumption: Object 1 is moving at the speed (V) near to the speed of light C (where V < C) and object 2 is static. Both objects have light clock where the distance between source/detector and mirror is d.

According to Einstein:

Time for static object 2: Δt2 = 2d/c
Time for moving object 1: Δt1 = (2d/c) x [1 / {1- (V^2/C^2)}^1/2]

So, Δt1 is higher than Δt2...(1)

Now according to me, there is no third frame in this case, for object 2 it can be considered as static and object 1 is moving.

Time for static object 1: Δt1 = 2d/c
Time for moving object 2: Δt2 = (2d/c) x [1 / {1- (V^2/C^2)}^1/2]

So, Δt2 is higher than Δt1...(2)

(1) and (2) cannot be true at same time.

Question: If Object 1 is moving at the speed (V) near to the speed of light (where V < C) and object 2 is static in real case, which object will have slowed down time in the light clock?

This question really need considerable thought process that may lead to the possibility where time will remain same for both clocks and there would not be any time dilation. It can be proved mathematically.

 

[FactChecker]

(1) and (2) cannot be true at same time.

This question really need considerable thought process that may lead to the possibility where time will remain same for both clocks and there would not be any time dilation. It can be proved mathematically.

You need to start from the fact that two physically separated events being "simultaneous" is not universally agreed upon. Suppose two reference frames are moving versus each other and each synchronizes clocks within its own inertial frame. Each frame's clocks tell it when two physically separated events are simultaneous. The two reference frames will not agree on simultaneity. So comparing two measurements of elapsed time is more complicated than you are imagining.

PS. You should be very cautious before you claim that all the geniuses have been wrong for the last 100 years -- and in such a simple way.

 

[PeroK]

(1) and (2) cannot be true at same time.

Yes they can. And they are. Time dilation is symmetric. Each observer measures the other's clock slower than their own.

To sort the mathematics, you need to be explicit about how quantities are measured.

A rough analogy is that if we are standing at opposite ends of a long room, I might hold out my arm and measure you as about the same height as my thumb. You might do the same. We both see each other smaller.

In any case, any introductory textbook on SR will explain the symmetry of time dilation and why it is not a paradox.

 

[FactChecker]

Suppose inertial frames A and B are moving versus each other and have synchronized their own clocks within their frame. Suppose that the clocks agree instantaniously at point X. Then at that instant ("instant" is porely defined, but I don't know a better way of saying this), the clocks disagree more and more at positions farther and farther from X in the direction of relative motion. Both frames are moving toward the trailing end of the other's frame, so each sees the same error in the other's clocks. Because of that, each sees the same time distortion (too slow) in the other's time.

 

[Ibix]

Thanks Dale! Here I am modifying the question for better understanding.

As noted by others, different reference frames do not agree what "starting two clocks at the same time" means. This ends up meaning that the time period you are calling $\Delta t1$ is not the same period in the two scenarios. Likewise $\Delta t2$. So your 1 and 2 are not contradictory - they only look it because you naively gave two different things the same labels.

You need to learn the Lorentz transforms, and specify the coordinates of the events at the beginning and end of each of your clocks' paths.

 

[Dale]

Time for static object 2: Δt2 = 2d/c
Time for moving object 1: Δt1 = (2d/c) x [1 / {1- (V^2/C^2)}^1/2]

So, Δt1 is higher than Δt2...(1)

Ok, this is all good.

Time for static object 1: Δt1 = 2d/c
Time for moving object 2: Δt2 = (2d/c) x [1 / {1- (V^2/C^2)}^1/2]

So, Δt2 is higher than Δt1...(2)

(1) and (2) cannot be true at same time.

Here it appears that you have changed frames to a reference frame where object 1 is stationary and object 2 is moving. There is nothing wrong with that, but you should always be clear and explicit when you change frames in your analysis.

You need to recognize that different frames will disagree about the time between different events. So if the time is Δt2 in one frame then it is not Δt2 in the other frame. Instead it is a different quantity which is usually denoted Δt2’ by convention.

Thus while you are correct that you cannot have both “Δt1 is higher than Δt2” and “Δt2 is higher than Δt1” that is not what relativity says. Instead, relativity says both “Δt1 is higher than Δt2” and “(Δt2’) is higher than (Δt1’)” which is perfectly acceptable

This question really need considerable thought process that may lead to the possibility where time will remain same for both clocks and there would not be any time dilation. It can be proved mathematically.

It can be proven both mathematically and experimentally that time dilation occurs.

 

[FactChecker]

So, Δt1 is higher than Δt2...(1)
So, Δt2 is higher than Δt1...(2)

(1) and (2) cannot be true at same time.

More accurate is:

So, Δt1 is higher than Δt2...(1) from observer 2's point of view.
So, Δt2 is higher than Δt1...(2) from observer 1's point of view.
So there is no contradiction and each observer can use SR to understand the other observer's point of view.

 

[Sandip Patel]

As noted by others, different reference frames do not agree what "starting two clocks at the same time" means. This ends up meaning that the time period you are calling $\Delta t1$ is not the same period in the two scenarios. Likewise $\Delta t2$. So your 1 and 2 are not contradictory - they only look it because you naively gave two different things the same labels.

You need to learn the Lorentz transforms, and specify the coordinates of the events at the beginning and end of each of your clocks' paths.

Let me simplify the question further that is the base of time dilation.

One object has laser source at front side (s1) and back side (s2). If that source travels from point X at the speed (v) near to the speed of light (v < c), where the front side is towards the direction of the motion and back side is at the opposite direction of the motion. What is the speed of light at front side (s1) and back side (s2) with reference to point x? Consider that all events are in same frame.

 

[phinds]

Let me simplify the question further that is the base of time dilation.

One object has laser source at front side (s1) and back side (s2). If that source travels from point X at the speed (v) near to the speed of light (v < c), where the front side is towards the direction of the motion and back side is at the opposite direction of the motion. What is the speed of light at front side (s1) and back side (s2) with reference to point x? Consider that all events are in same frame.

I have no idea what you are asking except the bolded part and I am flummoxed that you can be in any doubt what the answer to that is. The speed of light is c (assuming your setup is in a vacuum). Period.

 

[DaveC426913]

If that source travels from point X
...
Consider that all events are in same frame.

These two statements appear to be contradictory.
If the laser source is moving, then it is not in the same frame as x.

From which frame would you like to describe your observations?Also, as phinds points out, the only answer to "what is the speed of light (in a vacuum)?" is "c", regardless of any qualifiers you might add.

More to the point: Why do you think it would be different?

 

[Ibix]

Let me simplify the question further that is the base of time dilation.

One object has laser source at front side (s1) and back side (s2). If that source travels from point X at the speed (v) near to the speed of light (v < c), where the front side is towards the direction of the motion and back side is at the opposite direction of the motion. What is the speed of light at front side (s1) and back side (s2) with reference to point x? Consider that all events are in same frame.

As @phinds says, I have absolutely no idea why you go through a lengthy problem specification then ask something that is literally one of the fundamental postulates of relativity. The speed of light is always c in vacuum, under any circumstances.

Furthermore, "all events are in the same frame" is meaningless. Only descriptions are in one frame or another. Physical things just are. They can be described (probably differently) in any frame.

 

[Sandip Patel]

As @phinds says, I have absolutely no idea why you go through a lengthy problem specification then ask something that is literally one of the fundamental postulates of relativity. The speed of light is always c in vacuum, under any circumstances.

Furthermore, "all events are in the same frame" is meaningless. Only descriptions are in one frame or another. Physical things just are. They can be described (probably differently) in any frame.

Please refer below image for better understanding.

My question was what is the speed of light at s1 and s2 when the source is moving at speed (v) where v < c and near to c?

 

[FactChecker]

Let me simplify the question further that is the base of time dilation.

One object has laser source at front side (s1) and back side (s2). If that source travels from point X at the speed (v) near to the speed of light (v < c), where the front side is towards the direction of the motion and back side is at the opposite direction of the motion. What is the speed of light at front side (s1) and back side (s2) with reference to point x? Consider that all events are in same frame.

An outside "stationary" observer sees both lights traveling forward and backward at the same speed, c. The question is how a traveling observer can also measure equal speeds, c, in both directions. The answer is that, from the stationary point of view, his clocks are set wrong in the forward direction and are set with the opposite errors in the backward direction. So all the traveling measurements show the relative speed of light to be the same in both directions. The traveling measurement of distance is also distorted (with the same distortion in both directions) in a way that makes the speed exactly c in both directions.

 

[weirdoguy]

My question was what is the speed of light

c, always.

 

[Ibix]

Please refer below image for better understanding.

My question was what is the speed of light at s1 and s2 when the source is moving at speed (v) where v < c and near to c?

View attachment 234644

c. As I said. It's a postulate of relativity. As I also said, look up the Lorentz transforms. You can use them to understand all SR problems, and if you don't use them you'll probably never understand.

 

[Dale]

what is the speed of light at ...

c

 

[Sandip Patel]

Please refer below image for better understanding.

My question was what is the speed of light at s1 and s2 when the source is moving at speed (v) where v < c and near to c?

View attachment 234644

Edwin Hubble said universe is expanding at the speed faster than light. Galaxy at 14 billion light years are going far away from Earth at speed of light. Some galaxies farther than 14 billion light years cannot be seen by human as light will not reach to earth.

Why it will happen if you all say its only "C" my above question?

References:
https://www.space.com/33306-how-does-the-universe-expand-faster-than-light.html

https://www.loc.gov/rr/scitech/mysteries/universe.html

https://phys.org/news/2015-02-fast-universe.html

 

[PeroK]

Edwin Hubble said universe is expanding at the speed faster than light. Galaxy at 14 billion light years are going far away from Earth at speed of light. Some galaxies farther than 14 billion light years cannot be seen by human as light will not reach to earth.

Why it will happen if you all say its only "C" my above question?

View attachment 234648

References:
https://www.space.com/33306-how-does-the-universe-expand-faster-than-light.html

https://www.loc.gov/rr/scitech/mysteries/universe.html

https://phys.org/news/2015-02-fast-universe.html

Is this thread about time dilation or the expanding universe?

One thing at a time, please!

 

[Dale]

Why it will happen if you all say its only "C" my above question?

The second postulate states that the speed of light in vacuum is c in any inertial frame. There is no inertial frame that contains both the Earth and a galaxy 14 billion ly away.

The equivalent statement in GR is that light always travels on null geodesics. In inertial frames this statement reduces to the usual second postulate, but in non inertial frames it remains valid.

I strongly recommend that you stick with SR for now

 

[Ibix]

Why it will happen if you all say its only "C" my above question?

Because the concept of velocity of a distant object is a rather ambiguous one in curved spacetime. Invariably, you will find that the velocity of light as measured by a local observer is c. Distant observers can measure more or less any value, but it has no physical significance.

You are currently struggling with special relativity. You need to get that understood before you try seriously grappling with general relativity.

 

[phinds]

Edwin Hubble said universe is expanding at the speed faster than light.

To add to what others have already pointed out, you are confusing recession velocity, which is unlimited because nothing is "moving" in the sense you think it is, with actual proper motion which is where the limit of c applies. I agree w/ Dale. Let's drop consideration of the expanding universe (GR) since you apparently haven't studied it yet, and stick with special relativity.

EDIT: I see ibix beat me to it.

 

[nitsuj]

time dilatation happen, which watch will have slowed down time. Please help me understand the practical result if we have such case.

The practical result is called differential aging. To be specific, it's not really correct to say "slowed down", it's accurate to say one clock measured more time than the other. Some conceptualize this as a path; a distance measured.