Special Relativity and Light -- How does speed of an object affect time?

[BadgerBadger92]

TL;DR Summary

I am an amateur in physics and I have a question. How does speed of an object affect time? I recently started thinking that it’s due to light “not catching up” with the moving object, thus making time slow down. But what about the front?

Any help is appreciated. I think there are large gaps in my understanding so I would like some answers.

I am an amateur in physics and I have a question. How does speed of an object affect time?

 

[BvU]

Always good to ask curious questions. How about reading something introductory ? E.g. 'Special relativity for the enthusiastic beginner' by David Morin ?

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[BadgerBadger92]

Always good to ask curious questions. How about reading something introductory ? E.g. 'Special relativity for the enthusiastic beginner' by David Morin ?

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How about “Relativity in a way anyone can understand” by Einstein? Is that ideal for a beginner?

 

[PeroK]

Summary:: I am an amateur in physics and I have a question. How does speed of an object affect time? I recently started thinking that it’s due to light “not catching up” with the moving object, thus making time slow down. But what about the front?

Any help is appreciated. I think there are large gaps in my understanding so I would like some answers.

I am an amateur in physics and I have a question. How does speed of an object affect time?

The principle of relatively is that there is no concept in nature of absolute motion. Speed is relative and dependent on your choice of reference frame. The notion that "time depends on speed" is, therefore, a basic misconception.

What is true is that time is symmetrically dilated for two frames of reference in relative motion: each frame measures the other's time to run slow. There is no sense, however, that time in either frame is absolutely running slow.

 

[BvU]

How about “Relativity in a way anyone can understand” by Einstein? Is that ideal for a beginner?

Don't know about that and can't find it.

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[Nugatory]

How about “Relativity in a way anyone can understand” by Einstein? Is that ideal for a beginner?

Nothing by Einstein is going to be a good start. It’s not that he’ll be wrong (obviously) but rather that physics teachers have spent much of the past century knocking the rough edges off of his presentation and marking the path more clearly.

 

[PeterDonis]

Don't know about that and can't find it.

I believe he means this book:

https://www.amazon.com/dp/0517029618/?tag=pfamazon01-20

I agree with @Nugatory, however, that this is probably not the best introductory book about relativity for the layman. More modern presentations take into account a lot that we have learned in the past century that Einstein didn't know.

 

[BadgerBadger92]

Always good to ask curious questions. How about reading something introductory ? E.g. 'Special relativity for the enthusiastic beginner' by David Morin ?

Have you read this one? Is it any good?

 

[phinds]

How does speed of an object affect time?

It doesn't. You, as are all objects, are always moving through time at one second per second regardless of your speed. The confusion comes in when you talk about PERCEIVED time happening with an object that is in motion relative to you. IT perceives its time as one second per second but you may not, and as has already been mentioned, it's symmetrical --- if you see the object's time as slow, it sees your time as slow.

Gravitational time dilation is a different story.

 

[BadgerBadger92]

It doesn't. You, as are all objects, are always moving through time at one second per second regardless of your speed. The confusion comes in when you talk about PERCEIVED time happening with an object that is in motion relative to you. IT perceives its time as one second per second but you may not, and as has already been mentioned, it's symmetrical --- if you see the object's time as slow, it sees your time as slow.

Gravitational time dilation is a different story.

So time dilation is an illusion and not really traveling “forward” in time?

 

[Nugatory]

So time dilation is an illusion and not really traveling “forward” in time?

It is not an illusion and it not is traveling forward in time.

 

[BadgerBadger92]

It is not an illusion and it not is traveling forward in time.

What exactly do you mean by that?

 

[PeroK]

What exactly do you mean by that?

It's better to say simply what time dilation is. If we have an inertial reference frame and set a clock in uniform motion with speed $v$ relative to that reference frame, then we will measure the time on the clock to be dilated by a factor of $\sqrt{1 - \frac {v^2}{c^2}}$.

We can describe more precisely what we mean by the following experiment:

We have two clocks ($A$ and $B$) at rest, some distance apart and synchronised with each other in our frame of reference. We set a third clock ($C$) in motion, moving at speed $v$, as measured in our reference frame.

When clock $C$ passes clock $A$ we note the times shown. For simplicity, we can take $t_A = 0$ and $t_C = 0$ at this point. When clock $C$ passes clock $B$ we will find that:
$$t_C = \sqrt{1 - \frac {v^2}{c^2}}t_B$$ In other words, clock $C$ will read less than clock $B$. This is called time dilation.

 

[vanhees71]

Nothing by Einstein is going to be a good start. It’s not that he’ll be wrong (obviously) but rather that physics teachers have spent much of the past century knocking the rough edges off of his presentation and marking the path more clearly.

Among the most clearly written books about both SR and GR are Einstein's two books on the subject:

A. Einstein, The Meaning of Relativity
A. Einstein, Relativity: The special and the general theory

Another classic, using only the high-school math of the 1920ies, is

M. Born, Einstein's Theory of Relativity

Naturally these books, having been written in the 1920ies, are somewhat outdated in the way the theory is formulated but in no way in their contents.

 

[Ibix]

If I drive one mile due north, and you drive a few degrees west of north then when I say you are beside me your odometer will read more than a mile. Similarly, you will see me and my odometer reading one mile as beside you before your odometer reaches one mile. So we each say that the other's odometer advances more than a mile for each mile we advance forwards. Here it's obvious that nothing has "affected space", it's just that we aren't measuring parallel distances.

This is a very close analogy to time dilation. Relativity models space and time as a single entity called, imaginatively enough, spacetime and it turns out that clocks measure "distance" (technically called "interval") through it. Clocks in motion relative to one another are not following parallel paths through spacetime, so each clock says that the other advances less for each second it advances itself (not more, like in the odometer - spacetime is not exactly the same as space). But again, nothing has "affected time" (or space). The clocks are just being used to measure different intervals.

 

[robphy]

...So we each say that the other's odometer advances more than a mile for each mile we advance forwards. Here it's obvious that nothing has "affected space", it's just that we aren't measuring parallel distances.

This is a very close analogy to time dilation...
...Clocks in motion relative to one another are not following parallel paths through spacetime, so each clock says that the other advances less for each second it advances itself (not more, like in the odometer - spacetime is not exactly the same as space). But again, nothing has "affected time" (or space). The clocks are just being used to measure different intervals.

To complete this correct line of reasoning...
it needs to be said that, in the Galilean/Newtonian kinematics of PHY 101,
even though the compared segments (specifically the timelike-hypotenuse and timelike-side of the triangle) are not-parallel in a position-vs-time graph,
their elapsed proper-times are equal
---this is the meaning of "absolute time" in Galilean/Newtonian kinematics.

 

[cianfa72]

We have two clocks ($A$ and $B$) at rest, some distance apart and synchronised with each other in our frame of reference. We set a third clock ($C$) in motion, moving at speed $v$, as measured in our reference frame.

When clock $C$ passes clock $A$ we note the times shown. For simplicity, we can take $t_A = 0$ and $t_C = 0$ at this point. When clock $C$ passes clock $B$ we will find that:
$$t_C = \sqrt{1 - \frac {v^2}{c^2}}t_B$$ In other words, clock $C$ will read less than clock $B$. This is called time dilation.

Note that this process is not symmetric: we have 2 clocks ($A$ and $B$) at rest and Einstein synchronized in our reference frame plus another clock $C$ in motion at speed $v$ w.r.t. our reference frame.

From the other point of view we need 2 clocks ($C$ and $D$) at rest each other and just one clock ($A$ or $B$) moving with velocity $-v$ w.r.t. the rest frame of C and D clocks.

 

[BadgerBadger92]

So if spacetime isn’t changing what is to create this elapsed time?

 

[PeterDonis]

So if spacetime isn’t changing what is to create this elapsed time?

Why does there need to be anything to "create this elapsed time"?

You seem to have a mental model in which "time" is some kind of absolute thing. It isn't in relativity. There is no single absolute "time". There is just proper time along individual worldlines. Proper time is just arc length along a timelike curve, so all that "time dilation" really means is that different curves through spacetime can have different arc lengths.

 

[jartsa]

So if spacetime isn’t changing what is to create this elapsed time?

Let's say all those three clocks were made and calibrated in a factory, and let's say one of the clocks still ticks the same way as the big expensive atomic clock at the factory, according to witch all the produced clocks are calibrated at the factory. And two of the clocks do not tick at the same rate as the atomic clock.

We are talking about the three clocks that appear in post #13.

Now, in order to set up the experiment described in post #13, using clocks produced in the factory described here, the clocks produced in the factory have to go though big expensive clock accelerator machines. (Because the clocks have different speeds in the experiment.)

So I would say that it's those machines that create the difference. And the difference is in the clocks. And the important difference in the clocks is that they tick at different rates.

 

[PeroK]

So I would say that it's those machines that create the difference. And the difference is in the clocks. And the important difference in the clocks is that they tick at different rates.

The clocks are not physically affected by the acceleration. We could do the same experiment by accelerating clocks $A$ and $B$ and leaving clock $C$ alone. That would create the identical physical scenario.

Alternatively, as @cianfa72 points out, we could introduce a fourth clock $D$, which would be accelerated and brought to rest relative to clock $C$. This would give us a completely symmetrical scenario, where clocks $A, B$ and clocks $C,D$ are all moving inertially, with each pair moving at the same speed relative to the other pair. There is no physical experiment that could detect which ones have been accelerated and are "really" moving.

 

[cianfa72]

Alternatively, as @cianfa72 points out, we could introduce a fourth clock $D$, which would be accelerated and brought to rest relative to clock $C$. This would give us a completely symmetrical scenario, where clocks $A, B$ and clocks $C,D$ are all moving inertially, with each pair moving at the same speed relative to the other pair.

Thus clock $D$ undergone a (proper) acceleration and then brought to rest w.r.t. clock $C$. From this point onward all 4 clocks move inertially, with each pair moving at the same speed relative to the other pair.

There is no physical experiment that could detect which ones have been accelerated and are "really" moving.

You meant that, starting from the condition above, there is no physical experiment that could detect which ones have been accelerated and are "really" moving (sorry to repeat again your claim )

 

[Nugatory]

So if spacetime isn’t changing what is to create this elapsed time?

That’s like asking what creates the distance between two points in space - it doesn’t need to be created, it’s just there because they’re different points.

This analogy between distance in ordinary space and time in spacetime is useful: pick two points in space, and we use a meter stick to measure the distance (number of meters) between them; pick two points in spacetime and we use a clock to measure the time (number of seconds) between them. Different paths between the same two points in space have different lengths, and so do different paths between the same two points in spacetime: Suppose a spaceship takes off from Earth (that’s point A in spacetime), flies around for a while, and then returns to Earth (that’s point B in spacetime). A clock on the ship followed one path through spacetime to get from A to B, a clock on Earth followed a different path from A to B, the two clocks will have counted a different number of seconds along their different paths.

Of course no analogy is perfect. Ordinary space follows the rules of Euclidean geometry and spacetime is not Euclidean so times in spacetime aren’t related to one another the way distances in spacetime are. For example, in ordinary space the shortest path between two points is a straight line; in spacetime the straight line is the longest path.

 

[jartsa]

The clocks are not physically affected by the acceleration. We could do the same experiment by accelerating clocks $A$ and $B$ and leaving clock $C$ alone. That would create the identical physical scenario.

Alternatively, as @cianfa72 points out, we could introduce a fourth clock $D$, which would be accelerated and brought to rest relative to clock $C$. This would give us a completely symmetrical scenario, where clocks $A, B$ and clocks $C,D$ are all moving inertially, with each pair moving at the same speed relative to the other pair. There is no physical experiment that could detect which ones have been accelerated and are "really" moving.

Yes. I was talking about the non-physical difference between clocks moving differently. Like in special relativity we often talk about non-physical differences between objects moving differently.

Here are some examples of those non-physical differences: relativistic length, momentum, kinetic energy, charge distribution.

Also two objects moving differently is a non-physical difference, otherwise we could know if an object really moves or really stays still.

So I am saying that the "clock accelerator" changes a clock's relativistic ticking rate, but does not change its proper ticking rate. Just like the "clock accelerator" changes a clock's relativistic length, but does not change its proper length.

 

[Nugatory]

So I am saying that the "clock accelerator" changes a clock's relativistic ticking rate, but does not change its proper ticking rate. Just like the "clock accelerator" changes a clock's relativistic length, but does not change its proper length.

That is a rather amazingly confusing way of describing the unsurprising fact that when we choose different coordinate systems the numerical values of the coordinates will be different.

 

[PeroK]

@jartsa there is also the point that SR is most relevant to high energy particle experiments, where theoretically particles are created out of collisions and do not undergo an acceleration phase in order to make these non physical changes.

Time dilation and length contraction are related to the energy momentum transformations. We don't need acceleration in order to change from a lab frame to a COM frame and vice versa.

It is completely unnecessary to postulate an acceleration phase in order to identify time dilation, length contraction and energy momentum transformations between reference frames.

The clocks and particles themselves are blissfully unaware of our choice of reference frame.

 

[meekerdb]

In relativity thought experiments the clocks are always ideal clocks that run at exactly the same rate as could be confirmed by putting them side by side. The relativistic effects called "time dilation" are not affects on the clocks; they are due to moving the clocks along different paths in spacetime...and different paths between two events in general have different durations (4-lengths) just as paths thru space between two points have different lengths. The unintuitive part is because the metric signature has minus signs in spacetime (+ - - -) the straightest path is the longest instead of the shortest.

An excellent little book for gaining an intuitive understanding of relativity is "Relativity Visualized" by Lewis Carroll Epstein.

 

[Mister T]

How does speed of an object affect time? I recently started thinking that it’s due to light “not catching up” with the moving object, thus making time slow down. But what about the front?

You would be better off asking yourself what would prevent speed from affecting time. The reason you might think that speed can't affect time is based on some assumptions. Likewise, special relativity is based on some assumptions. It turns out the the latter matches what we observe in Nature's behavior much much better than the former.

 

[jartsa]

In relativity thought experiments the clocks are always ideal clocks that run at exactly the same rate as could be confirmed by putting them side by side. The relativistic effects called "time dilation" are not affects on the clocks; they are due to moving the clocks along different paths in spacetime...and different paths between two events in general have different durations (4-lengths) just as paths thru space between two points have different lengths.

Let's say you are given a picture of two analog watches side by side, there are two different vectors drawn, each vector starting from a different clock. Those are velocity vectors, that depict the velocities of the clocks.

Now you are given the task of drawing angular velocity vectors, that depict the angular velocities of the minute hands of the clocks. You don't draw identical vectors, right?

 

[BvU]

Right.

So ?

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[jartsa]

Right.

So ?

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As the angular velocities of the minute hands of those watches are different, then it follows that those two watches have different ticking rates, because ticking rate of a clock is proportional to the angular velocity of a clock-hand of said clock.

So clocks with different velocities have different ticking rates.

Velocity is a relative thing. Ticking rate is a relative thing.

 

[BvU]

Are you dangerously close to denying relativity altogether ? Good clocks have exactly the same ticking rates in their rest frames.

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[phinds]

As the angular velocities of the minute hands of those watches are different, then it follows that those two watches have different ticking rates, because ticking rate of a clock is proportional to the angular velocity of a clock-hand of said clock.

Uh ... you SERIOUSLY need to rethink that !

 

[PeroK]

And still it's correct. The fast moving hand is going somewhat slower in time. How can both time velocities keep up? If I find myself near a black hole, different parts of me move through time at different rates. My feet will move slower in time than my head. How will the flow of blood evolve? Will blood accumulate in some parts?

You don't need a black hole. As far as that makes sense, it applies when you're standing on Earth.

 

[PeterDonis]

As the angular velocities of the minute hands of those watches are different

They are different 4-vectors in spacetime, but they each have the same relationship to the corresponding 4-vectors in spacetime that describe the 4-velocities of the clocks. So each clock's "ticking rate" in its rest frame is the same, as @BvU has said.

And still it's correct. The fast moving hand is going somewhat slower in time.

No, it's not correct as he stated it. Each hand moves at the same speed relative to the clock it is attached to. See above.

You're changing the subject. We were talking about an ideal clock moving through space, not a physical clock in a gravity well.

But the situation is comparable.

No, the situation is not comparable. The GR effect you refer to is different from the SR effect under discussion in this thread. If you want to discuss the GR effect, please start a new thread.