Meaning of time dilation and length contraction

[robinpike]

When the phrases time dilation and length contraction are used, what do these really mean?

 

For example, say in the travelling twin paradox, there is a perceived time dilation that both twins observe happening to the other, as the travelling twin sets off (and a perceived time contraction as the twin returns).

 

I understand these meanings - perceived because it is a consequence of the twins moving away from each other, each twin observing the same perceived time dilation as the other.

 

But I have also seen time dilation being used as an actual time dilation - i.e. in the sense of 'rate of time' slowing down - and that I do not understand?

 

If the travelling twin really experienced a slow down in his rate of time, then by what action does his 'rate of time' return back to 'normal'?

 

The explanation that I have been given on this, is that the rate of time (not perceived) never changes for the travelling twin, but rather the distance of the travelling twin's space-time line is shorter than the stay at home twin's space-time line. So the travelling twin's rate of time does not change, but because his space-time line is shorter, his clock has gone through fewer 'ticks'.

 

This look a bit odd on a space-time diagram, as the travelling twin's space-time line looks longer on the diagram.

 

I do not understand space-time diagrams to know if that explanation is valid or not.

Could someone help and explain what a space-time diagram really represents and how this all works.

 

The same argument applies to length contraction - if actual length contraction really occurred, then by what action could the 'contracted length' return to 'normal'?

Edited October 16, 2014 by robinpike

[swansont]

There is no "normal" because there is no frame of reference you can absolutely choose as a standard, i.e. physics can't tell you oif you are at rest or if you are moving.

 

Two (ideal) clocks will run at the same rate if they are in the same reference frame (we're only looking at SR here; no gravitational effects)

 

So the twins' clocks will run at the same rate once the traveling twin returns to earth. However, the traveling twin will have accrued a time difference during the trip.

 

But since no frame is preferred, each person can say he is at rest (other than the period of acceleration). The other clock always looks like it's running slow. Length contraction is also true, which is how all the events can be reconciled. The traveling twin says his clock never slowed, but his trip was shorter.

[ajb]

If the travelling twin really experienced a slow down in his rate of time, then by what action does his 'rate of time' return back to 'normal'?

As far as each twin is concerned the rate of their own local time has not changed at all. This has to be the case otherwise the measurement of ones' own local time would depend on all the motion of all other objects in the Universe, not just the 'twin'.

 

I do not understand space-time diagrams to understand if that explanation is valid or not.

It is the space-time interval that you need to think about carefully. Both twins will agree on the distance they travel in space-time, but not separately space and time.

 

 

 

The same argument applies to length contraction - if actual length contraction really occurred, then by what action could the 'contracted length' return to 'normal'?

Exactly the same thing happens here as with time. You expect this as relativity more-or-less treats space and time on equal footing.

[Strange]

Part of the problem with the question is the meaning of the words "actual" and "perceived". The former implies something is more "real" (whatever that means) than the other.

 

But relativity is all about what we measure in one frame of reference from another frame of reference. When we measure (or calculate) the energy, length, rate at which clocks tick, etc. of an object in another frame of reference, we get a different value than if it was in our frame of reference. How do we know if that difference is real? Is one measurement more real than the other? Is the difference just a perception, an illusion?

 

Consider perspective, for example. Your friend in the distance looks smaller but you know here isn't "really" smaller, it is just an illusion. You could hold up a ruler and measure him as being 1 inch tall. But if he comes and stands next to you then you can tell he is "really" the same height he has always been.

 

Similarly, you might say that you will only consider time dilation or length contraction to be "real" if you can put your clock or ruler next to the object and measure it. But then you are in the same frame of reference, so the difference has disappeared.

 

(I still haven't decided if perspective is a good analogy or not, precisely because it isn't clear what "real" and "illusion" mean.)

 

I don't think I have helped answer the question (ajb's "it's the space-time interval" is a good answer). But perhaps I have explained why it may be a non-question.

[studiot]

 

Part of the problem with the question is the meaning of the words "actual" and "perceived". The former implies something is more "real" (whatever that means) than the other.

 

More or less exactly what I was considering saying +1

[Janus]

When the phrases time dilation and length contraction are used, what do these really mean?

 

For example, say in the travelling twin paradox, there is a perceived time dilation that both twins observe happening to the other, as the travelling twin sets off (and a perceived time contraction as the twin returns).

 

I understand these meanings - perceived because it is a consequence of the twins moving away from each other, each twin observing the same perceived time dilation as the other.

 

But I have also seen time dilation being used as an actual time dilation - i.e. in the sense of 'rate of time' slowing down - and that I do not understand?

 

If the travelling twin really experienced a slow down in his rate of time, then by what action does his 'rate of time' return back to 'normal'?

 

The explanation that I have been given on this, is that the rate of time (not perceived) never changes for the travelling twin, but rather the distance of the travelling twin's space-time line is shorter than the stay at home twin's space-time line. So the travelling twin's rate of time does not change, but because his space-time line is shorter, his clock has gone through fewer 'ticks'.

 

This look a bit odd on a space-time diagram, as the travelling twin's space-time line looks longer on the diagram.

 

I do not understand space-time diagrams to know if that explanation is valid or not.

 

Could someone help and explain what a space-time diagram really represents and how this all works.

 

 

The same argument applies to length contraction - if actual length contraction really occurred, then by what action could the 'contracted length' return to 'normal'?

Here are a couple of Space-time diagrams illustrating both the perceived Doppler effect and Relativistic time dilation.

 

Time is the vertical direction and space the horizontal. Anything on the same horizontal line are simultaneous. A 45 degree angle represents light speed.

 

The Blue line represents one twin and the Green line the other. The yellow lines are light. The left image are events according to the Blue twin, and the right image the same events according to the Green twin. The twins start off some distance from each other, meet when both their clocks read zero and then separate again.

 

 

If we look at the left image, we see that When blue's clock reads -3, it sends the light carrying this information reaches Green when Green's clock reads -1.5. The light from Blue reading -2 reaches Green when Green reads -1, and the light from Blue reading -1 reaches Green when Green reads -0.5. In other words, Green sees Blue's clock go from -3 to -1 while his own goes from -1.5 to -0.5. Green sees Blue's clock run twice as fast.

 

You will also note the the same goes for the light leaving Green and arriving at Blue. Blue sees Green's clock tick away twice as fast.

 

Once they meet and separate, the reverse happens, Blue sees Green's clock tick 1/2 as fast and Green sees Blue's clock tick 1/2 as fast.

 

This takes care of the Doppler shift aspect.

 

Now on to time dilation. If you draw a line horizontally across from where blue's clock reads -3, you see it intersects green somewhere between Green's clock between -3 and -2 (-2.4 to be exact) This represents the time for Green at this instant according to Blue. When Blue's clock reads -2, Green reads -1.6, etc. So in the time it takes for Blue's clock to tick from -3 to 0, Green's clock ticks from -2.4 to 0, So according to Blue, Green's clock ticks 0.8 as fast as his own. This is Relativistic time dilation. It is what is "left over" after you account for light travel time in what you see due to the Doppler effect.

 

Note that this remains unchanged after the two meet. According to Blue, Green's clock still ticks slower than his own.

 

Now, unlike the Doppler effect, we cannot use this same image to extrapolate how fast Blue's clock runs according to Green. Here's why: Above we said that Time dilation is is what is left over after account for light signal delay with the Doppler shift. Basically, this means you could work backward from the Doppler shift to get time dilation. Basically, if Blue sees Green read 2 when his clock reads 1, and he knows that they meet when the clocks read Zero, and knows the their relative velocity, he can "backtrack" the light signal to figure out when it left Green by his clock. In the diagram these light signals are drawn at 45 degree angles to Blue's line.

 

Sine the speed of light is invariant, to sees things from Green's perspective, we have to draw the light signal lines at a 45 degree angle to Greens line. The easiest way to do this is to rotate the Image so green goes straight up and the draw the 45 degree light lines.

 

Now we have already established the times of emission for each and the time's of recepetion of those signals, and those must stay the same. Thus if blue sees green read -2 when His own clock reads -1 in the left image, this must also must be true for the right image. For this to be true for all such events and the angle for the light signal to remain at 45 degrees, we end up with the image on the right for how events transpire for green.

 

This basically turns out to be a mirror image of the left image with the Blue and Green line's swapped.

 

All the events of what each twin sees remain the same, they each see the other clock running fast when approaching and running slow when receding.

 

But now it is Blue's clock that runs slow according to time dilation.

 

Basically, The difference between Doppler shift and time dilation, is between what you see due to light propagation delay vs what is happening "right now".

 

And while we are on the subject of "right now". These images also demonstrate the Relativity of Simultaneity. Look again at the left image and the horizontal line where Blue reads -3. As we noted, this occurs when Green reads -2.4. So according to Blue, the events of his own clock reading -3 and Green's clock reading -2.4 are simultaneous.

 

Now look at the right image, again draw a horizontal line across from where Blue reads -3. It crosses Green somewhere between -3 and -4(-3.75) this means that according to Green, the event of Blue reading -3 and his own clock reading -2.4, are not simultaneous. When Blue reads three, his clock reads 4.75, and when his clock reads 2.4, Blue's clock reads 1.92.

 

o there you have it, The twin's agree on what each other see, But they don't agree as too what is happening to each others clocks at any given moment.

 

If you were doing the standard twin paradox, you have one twin changing velocity halfway through, and this is like jumping from the viewpoint of Blue to Green in the example above. (basically, after changing velocity the twin's assessment of what is or is not simultaneous will change, While it does not for the twin who does not change velocities.)

[robinpike]

Thank you Janus for the help on the space-time diagram (and the others on this topic), it will take me a little while to digest the information as there is quite a lot to take in.

 

As regards the meaning of 'actual' and 'perceived', if two view points are contradictory, then at least one of those view points must be perceived and not actual.

 

For example if twin A sees twin B's clock run slower, and twin B sees twin A's clock run slower, then at least one of their view points must be perceived and not real.

 

This deduction is of the form: If A > B and B > A, then one of those statements must be false.

 

The result of line of sight and perspective is a simple example of the above. Twin A and twin B stand next to each other and note that they are of the same height. Twin A walks away from twin B and after a while, turns around and sees that he can obscure his view of twin B by holding up his thumb in front of his line of sight - with a perceived sense that his twin is now smaller than he is.

 

Twin A can also do the same to his view of twin B - with a perceived sense that his twin is now smaller than he is.

 

Both of these situations cannot be true, at least one must be false. In this example, both are false as the twins are still the same height as each other, the perceived effect is down to perspective.

 

In relativity and the twin paradox, after the twin B's journey, his clock has less time on it, so we know something happened to his time - an actual change has occurred.

 

The reason why I want understand the space-time diagram, is because the loss in time of the travelling twin's clock cannot be due to a slowing down of time of his clock - that must be only a perceived effect.

 

The reason being that if the travelling twin's clock were slowed down, i.e. a slow down in his rate of time, relativity has no means of returning that rate of time back to 'normal'. I.e. when he returns back to earth and their two clocks are seen to be running at the same rate, but the travelling twin's clock has a lesser time on it.

 

There is no difference between acceleration and de-acceleration in relativity. If acceleration were to slow down a clock for real, then de-acceleration would also slow down the clock for real (according to relativity).

 

My understanding of this is that 'the rate of time' never changes for the travelling twin. But he did lose time on his clock. This is why I want to understand the space-time diagram, as when in the past I have discussed the above point on acceleration / de-acceleration, it was mentioned that the space-time diagram explains how the travelling twin lost time on his clock.

 

And this is what I want to understand.

Edited October 20, 2014 by robinpike

[ajb]

As regards the meaning of 'actual' and 'perceived', if two view points are contradictory, then at least one of those view points must be perceived and not actual.

Measurements are measurements and are not contradictory, they do however depend on the 'rulers and clocks' you use; meaning that they can depend on the inertial reference frames employed. Related to this is the notion of simultaneity and how it is not an invariant notion.

 

Anyway, for absolute events the observers will agree, but not necessarily on 'when and were'. For example, if some heavy particle decays into two lighter one in its rest frame then it will be seen to decay in all other inertial frames. The observers may disagree on when it decayed, they have 'different clocks' but for sure they all agree that it did decay.

[studiot]

One thing to remember is there is a difference between the way length, mass and time work.

 

If you take a twin on a round trip length, mass and time will measure differently during the trip.

 

But when they return and the two twins are again side by side only age is different.

 

Both mass and size return to their original figures (space diets aside) but the twin's ages are now different.

[swansont]

 

As regards the meaning of 'actual' and 'perceived', if two view points are contradictory, then at least one of those view points must be perceived and not actual.

 

That's an issue under the assumption that there is an absolute frame of reference. But the "contradictions" show that that is a bad assumption and must be discarded.

 

Either observer, making measurements and doing calculations in his/her own frame, will get the same result for a physics problem, even though individual measurements (e.g. time and length) will not agree

The reason being that if the travelling twin's clock were slowed down, i.e. a slow down in his rate of time, relativity has no means of returning that rate of time back to 'normal'. I.e. when he returns back to earth and their two clocks are seen to be running at the same rate, but the travelling twin's clock has a lesser time on it.

 

There is no difference between acceleration and de-acceleration in relativity. If acceleration were to slow down a clock for real, then de-acceleration would also slow down the clock for real (according to relativity).

 

 

Changing the rate and changing the accumulated time are not the same thing. The time is the integral of the rate.

 

Acceleration has nothing to do with this. In the twins example, the acceleration is usually assumed to be instantaneous so there is no accumulated effect. All the acceleration does is change the relative speed, i.e. change the frame. It's the speed that determines the amount of slowing. If the acceleration reduces the relative speed, then the clock (as observed by the one in the other frame) will speed up.

[studiot]

 

There is no difference between acceleration and de-acceleration in relativity. If acceleration were to slow down a clock for real, then de-acceleration would also slow down the clock for real (according to relativity).

 

As swansont noted, it is the relative velocity that is important here.

 

B says that A travels away with r. velocity +V and makes the return trip with r velocity -V.

 

However A could say that B travels away with r.velocity -V and returns with r.velocity +V.

 

This makes no difference since the gamma factor depends upon the velocity squared.

Edited October 20, 2014 by studiot

[phyti]

When the phrases time dilation and length contraction are used, what do these really mean?

 

For example, say in the travelling twin paradox, there is a perceived time dilation that both twins observe happening to the other, as the travelling twin sets off (and a perceived time contraction as the twin returns).

 

I understand these meanings - perceived because it is a consequence of the twins moving away from each other, each twin observing the same perceived time dilation as the other.

 

But I have also seen time dilation being used as an actual time dilation - i.e. in the sense of 'rate of time' slowing down - and that I do not understand?

 

If the travelling twin really experienced a slow down in his rate of time, then by what action does his 'rate of time' return back to 'normal'?

 

The explanation that I have been given on this, is that the rate of time (not perceived) never changes for the travelling twin, but rather the distance of the travelling twin's space-time line is shorter than the stay at home twin's space-time line. So the travelling twin's rate of time does not change, but because his space-time line is shorter, his clock has gone through fewer 'ticks'.

 

This look a bit odd on a space-time diagram, as the travelling twin's space-time line looks longer on the diagram.

 

I do not understand space-time diagrams to know if that explanation is valid or not.

Could someone help and explain what a space-time diagram really represents and how this all works.

 

Maybe this will help.

Time dilation and aging for a pair of clocks.doc