Is velocity the reason for the time dilation effect?

[Mike_bb]

Hello!

I try to understand how in different frames clocks tick and stop simultaneously but show different time? I suppose that velocity is reason of time dilation effect but I'm not sure.

Thanks.

 

[vanhees71]

A clock always shows its "proper time". For a clock moving along an arbitrary (necessarily time-like) world line the relation to the time of an arbitrary inertial frame, wrt. you consider the motion of the clock, you have
$$\mathrm{d} \tau=\mathrm{d} t \sqrt{1-\vec{v}^2/c^2},$$
i.e., time dilation, i.e., the fact that for a moving clock the proper time (i.e., the time as observed by an observer at rest relative to the clock) is always running slower than the coordinate time of the inertial frame, relative to which its motion is considered.

If the clock is moving with constant velocity you can immediately integrate the equation, i.e., then you have $\vec{v}=\text{const}$ and you get (assuming that we set $\tau=0$ for $t=0$)
$$\tau=t \sqrt{1-\vec{v}^2/c^2} \; \Leftrightarrow \; t=\frac{\tau}{\sqrt{1-\vec{v}^2/c^2}}.$$

 

[Mike_bb]

Does velocity contribute to the time dilation effect?

 

[jbriggs444]

Does velocity contribute to the time dilation effect?

What do you think the "time dilation effect" is?

 

[Mike_bb]

What do you think the "time dilation effect" is?

Time dilation is the difference in elapsed time as measured by two clocks due to a relative velocity between them

 

[Nugatory]

Does velocity contribute to the time dilation effect?

Velocity does appear in the time dilation formula, the greater the velocity the greater the effect, so yes, velocity is pretty clearly involved. However, we have to be clear that it is relative velocity that matters here.

If we have two identically constructed clocks A and B, and they are moving relative to one another:
- Someone at rest relative to clock A will find that clock A is running normally while clock B is running slower than A.
- Someone at rest relative to clock B will find that clock B is running normally while clock A is running slower than B.
- They are both right.

 

[jbriggs444]

Time dilation is the difference in elapsed time as measured by two clocks due to a relative velocity between them

So... simultaneous start on the two clocks? Simultaneous stop on the two clocks? Unaccelerated motion for each clock? Difference in their respective elapsed times upon being stopped?

This velocity of which you speak. Not frame relative. That is good. But... how do we know which clock is "slow" and which is "fast"?

This simultaneity of which you speak. Measured how?

 

[Mike_bb]

So... simultaneous start on the two clocks? Simultaneous stop on the two clocks?
This simultaneity of which you speak. Measured how?

For example, light clock and mechanical clocks. We can simultaneously start mechanical clocks at initial point and if light reach to end point we can stop simultaneously our mechanical clocks in different frames.

 

[jbriggs444]

For example, light clock and mechanical clocks. We can simultaneously start mechanical clocks at initial point and if light reach to end point we can stop simultaneously our mechanical clocks in different frames.

No. We cannot. Light clocks, mechanical clocks and all other clocks are subject to a slew in measured simultaneity based on frame of reference.

 

[Mike_bb]

No. We cannot. Light clocks, mechanical clocks and all other clocks are subject to a slew in measured simultaneity based on frame of reference.

I read that light reach to end point simultaneously in different frames.

 

[Nugatory]

I read that light reach to end point simultaneously in different frames.

If two events are simultaneous in one frame, they are in general not simultaneous in other frames, and that’s why you must be much more careful about saying that things are happening “simultaneously” - which frame matters.
This is the relativity of simultaneity, a crucial piece of relativity that is unfortunately skipped over in many popular books/articles on relativity.

There is no way to make sense of time dilation and length contraction without also understanding relativity of simultaneity. The three work together to keep everything consistent.

 

[Dale]

I read that light reach to end point simultaneously in different frames.

Where exactly did you read this? It would help us to know if you are misunderstanding a good source or correctly understanding a bad source.

 

[Mike_bb]

If two events are simultaneous in one frame, they are in general not simultaneous in other frames,

I mean another. I mean that in moving frame and in non-moving frame same event happens simultaneously.

Where exactly did you read this? It would help us to know if you are misunderstanding a good source or correctly understanding a bad source.

Ok. For example, light clock. Light reach to end point simultaneously in non-moving and moving frames.
https://en.wikipedia.org/wiki/Time_dilation#Simple_inference

 

[Dale]

Ok. For example, light clock. Light reach to end point simultaneously in non-moving and moving frames.
https://en.wikipedia.org/wiki/Time_dilation#Simple_inference

Ok, this is a good reference. Nowhere does it say:

light reach to end point simultaneously in different frames.

”Simultaneous” is a comparison between two events with respect to one reference frame. If, in a given frame, the two events have the same $t$ coordinate, then we say that the events are simultaneous in that frame.

 

[Mike_bb]

Ok, this is a good reference. Nowhere does it say:

Another example is the propagation of light from the middle of a moving train to its left and right
ends. From the train passenger's point of view, the light will simultaneously reach the right and left ends of the train, with point of view of an outside observer - at different times.

In this example, light reach left end of train with point of view of passenger and with point of view of outside observer simultaneously. Is it true?

 

[FactChecker]

The word "simultaneous" is tricky in SR. Suppose the light starts where each frame has a clock and those clocks are both reading time=0. Suppose each frame has clocks that are synchronized in that frame. The moving frame goes some distance while the light travels. Then the light hits the end where each frame has a clock. Those two clocks do not record the same time. It is tricky to call it "simultaneous" in those frames, since that usually means "at the same time" whereas the clocks indicate different times. This is called the "relativity of simultaneity".
Any time you use the word "simultaneous" in SR, you must indicate the inertial reference frame that considers those two events to be simultaneous.

 

[jbriggs444]

I mean another. I mean that in moving frame and in non-moving frame same event happens simultaneously.

"Simultaneus" is not normally an adjective used to refer to one event viewed from two reference frames.

Even if two frames are synchronous (share the same time coordinate) at one event along a world line, they will not normally be syntonous (sharing the same time rate) along that world line.

 

[Mike_bb]

The word "simultaneous" is tricky in SR. Suppose the light starts where each frame has a clock and those clocks are both reading time=0. Suppose each frame has clocks that are synchronized in that frame. The moving frame goes some distance while the light travels. Then the light hits the end where each frame has a clock. Those two clocks do not record the same time. It is tricky to call it "simultaneous" in those frames, since that usually means "at the same time" whereas the clocks indicate different times. This is called the "relativity of simultaneity".
Any time you use the word "simultaneous" in SR, you must indicate the inertial reference frame that considers those two events to be simultaneous.

Is it true that in previous example light reach left end of train with point of view of passenger and with point of view of outside observer simultaneously?

 

[vanhees71]

You contradict yourself. Your first paragraph has it right: For the train passenger the light signal reaches the ends of the train at the same time ("simultaneously"), for the observer on the embarkment at different times, and indeed this is called the "relativity of simultaneity".

This is one of the few examples, where it really helps to draw a Minkowski diagram:

The primed reference frame is the rest frame of the train. The passenger in the train sits in the origin, i.e., in the middle of the train and sends a lightsignal at time $t'=0$. His wordline is the $t'$ axis. From the point of view of the passenger light signal reaches the ends of the train (blue world lines) at times $t_+'=t_-'$, i.e., simultaneously.

The observer on the embarkment is at rest in the unprimed frame, and clearly the light signal reaches both ends at different times $t_-<t_+$. That's also intuitively clear, because also from his point of view the light signal propagates with the speed of light in vacuo, $c$, although the light source is moving with respect to him. Now the one end moves towards the light source and the other away from the light source, i.e., the signal needs less time to reach the former than the latter end of the train.

 

[FactChecker]

Is it true that in previous example light reach left end of train with point of view of passenger and with point of view of outside observer simultaneously?

When you say it was "simultaneous" from both points of view, that usually means "at the same time". But the clocks of the two observers indicate different times.

 

[FactChecker]

Is it true that in previous example light reach left end of train with point of view of passenger and with point of view of outside observer simultaneously?

It is one event being recorded in two different ways.

 

[Dale]

Another example is the propagation of light from the middle of a moving train to its left and right
ends. From the train passenger's point of view, the light will simultaneously reach the right and left ends of the train

Yes. This is two events, the light reaches the left end and the light reaches the right end. In the passenger’s frame they occur at the same $t$ so they are simultaneous.

with point of view of an outside observer - at different times

Yes. The same two events have different $t$ coordinates in the ground’s frame. So they are not simultaneous in this frame.

Events which are simultaneous in one frame are not simultaneous in other frames.

In this example, light reach left end of train with point of view of passenger and with point of view of outside observer simultaneously. Is it true?

No, this is not true. As I said above ”simultaneous” is a comparison between two events with respect to one reference frame. If, in a given frame, the two events have the same coordinate, then we say that the events are simultaneous in that frame.

Here you have one event, light reaching the left end, and two frames the passenger’s and the ground’s. The concept of simultaneity doesn’t even fit.

 

[Mike_bb]

When you say it was "simultaneous" from both points of view, that usually means "at the same time". But the clocks of the two observers indicate different times.

Yes. I used this term wrong. I don't mean about "time simultaneous" or "at the same time". I mean that when light reach to end of train with point of view of passenger then light reach to end of train with point of view of observer. Is it true?

 

[PeterDonis]

I mean that when light reach to end of train with point of view of passenger then light reach to end of train with point of view of observer. Is it true?

Your question is not well-defined. The event where the light reaches the end of the train is a specific point in spacetime: it's the same point for all observers. But the time coordinate assigned to that event is different for the train passenger and the observer. It's not clear which of these you are asking about.

 

[Mike_bb]

Your question is not well-defined. The event where the light reaches the end of the train is a specific point in spacetime: it's the same point for all observers. But the time coordinate assigned to that event is different for the train passenger and the observer. It's not clear which of these you are asking about.

Yes. And I want to understand how is it possible that time coordinate assigned to that event is different for the train passenger and the observer. What is reason of this thing?

 

[PeterDonis]

I want to understand how is it possible that time coordinate assigned to that event is different for the train passenger and the observer. What is reason of this thing?

Mathematically, the simplest way to see it is to take the coordinates of the event in one frame and Lorentz transform them into the other frame. The Lorentz transformation changes the time coordinate.

 

[jbriggs444]

Is it true that in previous example light reach left end of train with point of view of passenger and with point of view of outside observer simultaneously?

What does that even mean? What does it mean for one event to be simultaneous with itself?

 

[Mike_bb]

Thanks to all!

 

[David Lewis]

Suppose the light starts where each frame has a clock and those clocks are both reading time=0. Suppose each frame has clocks that are synchronized in that frame. The moving frame goes some distance while the light travels. Then the light hits the end where each frame has a clock. Those two clocks do not record the same time.

I think both clocks will record the same time in all frames. The flash bulb is equidistant between the two clocks, and the clocks are synchronized*, so the reading on both clock faces will show that the light hit them at the same time.

* In the train frame

 

[Ibix]

I think both clocks will record the same time in all frames. The flash bulb is equidistant between the two clocks, and the clocks are synchronized*, so the reading on both clock faces will show that the light hit them at the same time.

* In the train frame

I think @FactChecker is considering two events, one when light is emitted and one when the light is absorbed at another location. The time between those events is different in different frames.

You, on the other hand, seem to be considering three events, one where light is emitted and two where the pulse is absorbed. If clocks at the two absorption events are synchronised in the frame where those events are equidistant from the emission event then they will record the same time, yes.