# Explanation of time dilation due to c being the maximum speed

1. Nov 25, 2015

### MachPrincipe

I have seen a video in which the time dilation due to velocity is explained by saying that light and light interactions inside a moving body must travel a longer distance in space, which reduces the passage of time.

Video:

This explanation is new to me, and in fact, I recently heard an almost identical one a few months ago. Til now I have always considered that time itself was affected by speed, and that what is described above was more a consequence (effect) than a cause. As most, they would be equivalent.

I am suspecting that this kind of explanation comes from some relatively recent book or other science divulgation media, which has popularized this view.

I have these objections to that explanation, and because I am too used to the usual, conventional, explanation, would be very glad that someone can correct me if I am wrong in some of my objections.

My objections are these:
1. Time dilation is a consequence coming directly from the 2 postulates. Lorentz transformations apply and we have time dilation, which affects directly to rate of clocks.
2. Time is "going slower" (time dilation) for the moving object, i. e., the proper time of the (moving) ship is shortened respect to (rest) Earth.
3. In the explanation due to speed interactions (video and similar ones), it is assumed that there exists a maximum speed, that this speed is that of light, and that time emerges from this maximum speed, so for particles distant each other, and moving, it will take a longer time to communicate, and the passage of time will be lesser for these particles. Also that all sorts of interactions, even subatomic, will attain to this speed.
4. All the assumptions in point 3 are derived from the result of c = maximum speed, which comes from Lorentz transf. if we start with the 2 postulates, so indeed we are already stating that time dilation applies (circularity).
5. For a muon, and its spontaneous radioactive decay, being a point particle and the decay a stochastic quantum process, the explanation of maximum speed would not seem to apply and would not explain the dilatation which allows them to travel through the entire atmosphere of the Earth. Time dilation explains it.
6. As for transveral Doppler effect, I am not sure if the interpretation of maximum speed of light would explain it, but slower time passage does, directly (this I am not sure).
My sensation with this explanation is that it is closer to the Lorentzian interpretation of relativity, rather than actual Einstenian relativity.

Suggestions are appreciated.

2. Nov 25, 2015

### phinds

Just a quick comment on that aspect of your statements. Time is going slower for the moving object relative to Earth, yes, but likewise the time on the Earth is going slower for the observer on the spaceship. Proper time does NOT slow down for either one. Proper time for the traveler is what is measured in a reference frame in which the traveler is at rest and proper time for the Earthbound is what is measured in the reference frame in which the Earth bound person is at rest. Both proper times are ticking at one second per second. Of course, if the traveler turns around and comes back, he will have experienced a different number of seconds but that's differential aging, not time dilation per se.

3. Nov 25, 2015

### MachPrincipe

Yes, you are completely right. I was refering to proper time (clock at rest aboard the ship) and coordinate time (clock at rest in Earth). Also agree on the reciprocity of both systems. As for the interpretation, minute 5 of video, and my interpretation and judgement of it, what do you think?

4. Nov 25, 2015

### Staff: Mentor

They may be referring to a "light clock", which is one of the simplest models in which one can see how the invariant speed of light leads to the prediction of time dilation. This article gives a reasonably simple presentation:

http://galileoandeinstein.physics.virginia.edu/lectures/srelwhat.html

Why not?

Transverse Doppler is a consequence of the Lorentz transformations, just like time dilation.

5. Nov 25, 2015

### MachPrincipe

And it is lengthened, not shortened. Two seconds or ticks in the moving clock ta
I am not succeeding at explaining me. I do not claim that TDE is not coming from Lorentz transformations. I am not claiming that muon extended half life does not happen. I say that the video is, implicitly or explicitly, that time itself is not affected by speed. The interpretation is that bodily processes (in the brain, in other organs, inside the computer aboard) are slowed because the light and any other interacting medium has this maximum speed, c, and thus everything goes slower, time is like freezing. This would consider time as an emerging property. Thus, processes where electromagnetic signals are not involved, or where there are no distances for the information to travel, like a pointlike particle as a muon decaying, the explanation, analogy or whatever you call this explanation is not appliable. In contrast, time by itself being delayed is what would explain this delayed decay. Also about the transverse Doppler, I do not see right now how longitudinal speed can affect in this interpretation,, while effective slowing of time does. In fact, longitudinal Doppler effect has a mixture of classical and time dilation and transverse Doppler is purely relativistic. By as the new interpretation is in fact, right about maximum speed, this is why I consider it to be quite equivalent in predictions, but with the points of circularity, limitations for muon, etc, etc.

6. Nov 25, 2015

### Mister T

It appears to be an application of the same effect described by the traditional analysis of a light clock. However, they get it wrong. At about the 6-minute mark they mention that people in the rocket are traveling "closer to the speed of light" than people on Earth. That is simply false and contradicts both postulates. To see that their explanation is preposterous, note that they cannot use it to explain why people on the rocket will observe clocks on Earth running slow. According to their arguments, people on Earth will be seen to have their clocks running faster because the subatomic particles in their bodies have a shorter distance to travel than the ones in people on the rocket. And for that reason people on Earth age faster than people on the rocket.

That is an inaccurate depiction of the difference in proper time experienced by the twins in the twin paradox. The correct explanation involves the asymmetry in their paths through spacetime, and in the video there is no mention of that asymmetry, only the erroneous closer-to-c asymmetry I mentioned. A valid explanation of the twin paradox involves at least some reference to a valid asymmetry, otherwise one is limited to describing things only from the viewpoint of the one twin who's inertial and avoiding the fact that the same analysis won't work for the noninertial twin. One must at least mention the fact that it won't work

I do not think the video presents anything of substance that hasn't already been presented by others. Those mistakes have been around as long as people have been describing Einstein's relativity, and they will likely continue to be created in ways that might seem new but perhaps aren't.

Last edited: Nov 25, 2015
7. Nov 25, 2015

### MachPrincipe

I missed the part of the nearest to c - my native language is not English. But then, please read what I recall from a friend in a dinner: he explained time dilation this way: imagine a ship going at c minus a very small quantity. As it travels so fast, when they turn on a lamp in the rear part, it will take ages for the light to reach the front part. As c is constant, time must be frozen in the ship or they would measure a very slow light speed.
That explanation is symmetrical and simpler than usual light clock analysis, maybe because you pretend to get the idea, not the formula. The novelty here would be to associate the light interaction with «time flow» itself. In any case, he (video author) does not explain lenth contraction either, not relativity of simultaneity.

8. Nov 25, 2015

### phinds

That's just silly. I'm assuming that's your point, that your friend has it all wrong.

9. Nov 25, 2015

### Mister T

Let's say it's a very very long ship (1 light second long, or 300 000 km) so it takes the light flash one second to go from the rear of the ship to the front.

Suppose the ship is moving at a speed of 0.96c relative to someone watching it pass. In that person's frame of reference it will travel a distance of 7 light seconds and so take 7 seconds to reach the front of the ship.

Since MachPrincipe tells us his native language is not English, I took his use of the word frozen to mean sluggish, or slow. I could be wrong.

I believe that this is the phenomenon the producers of the video were trying to describe, but they buggered it up.

Last edited: Nov 25, 2015
10. Nov 25, 2015

### MachPrincipe

Well, in fact you can retain a normal length, ten meters, and put an absurd speed, let's say 0.999999999999......99999c. First, you will have a very noticeable length contraction, which is never mentioned, but it is clear that light will take a lot of time to reach the front end. In order to keep this a low proper time, time will go so slowly as to appear almost frozen. In fact, this is exactly the light clock idea, but carried to the extreme and without calculations being important, it is just for dramatic purposes, to convince of the time dilation effect. It is the other assumption which bothers me: that it is not time by itself which goes slower due to speed, but it is the difficulty, let's say so, of interaction of particles with each other which makes time to appear almost frozen. It is a very subtle assumption, I have read it in other posts somewhere in internet, and I think it is wrong and circular.

11. Nov 26, 2015

### Mister T

The numbers I posted take length contraction into account. If you had a ship length of 300 m, the time on the ship would be one microsecond, and the time measured by the observer would seven microseconds.

The light clock scenario need not include any calculations. It's more obvious to me because it doesn't involve length contraction. That's the beauty of it.

It is in fact a mechanism. One must use some mechanism to introduce the notion of time dilation. Then make the argument that if that mechanism measures time, then all other time-measuring mechanisms will give the same result. From there it's a philosophical issue that we're dealing with time itself rather than a measurement of time.

12. Nov 26, 2015

### Staff: Mentor

This does seem dubious. It also seems unnecessary; the argument using the invariant speed of light is already sufficient.

13. Nov 28, 2015

### MachPrincipe

I agree. Summarising some of the comments, I have the following view:

Light clock can be used to show the time dilation. Applied in a direction transversal to the path, no length contraction is needed to show that there exists a time dilation. Of course, this popular explanation does not proof the time dilation concept, but shows an easy example of it.

The concept in the video seems to be a popular way of explaining time dilation. It ignores length contraction, so it is rather poor as an explanation. It uses a modified version of the light clock explanation, using not a tranversal direction but a longitudinal direction (this is why the ignored length contraction should be needed. It would complicate the explanation, so this is why this is not a satisfactory way of explaining the effect, at least if you do not make some maths).

The concept of time dilation being an emerging property associated with "time flow" itself is a philosophical concept more than a scientific one. It has its own problems. Trying to reconcile the idea with a Lorentzian view of relativity is a bad idea, as the main achievement of special relativity is to make all considerations of Lorentzian POV superfluous and unnecesary (Lorentz introduced a time which was more a mathematical artifact than a "real" time).

That said, I found again this reference. Many years ago I found it and read it, but I never bought the idea. Now it re-surfaces again. I think it is associated with the concept (badly expressed in the popular video).

Direct calculation of time dilation, Oleg D. Jefimenko, Am. J. Phys. 64, 812 (1996)

14. Nov 28, 2015

### Mister T

It demonstrates that time dilation is a consequence of the two postulates. Demonstrating that a conclusion follows from a set of premises is the usual definition of a proof.
That demonstration of time dilation is valid. It's the same as the one given by your friend where the light signal is sent from the rear of a moving ship to the front. It doesn't mention length contraction, so in that sense it ignores it, but it is nevertheless there. It just goes unmentioned. The problem in the video is that they are treating the dilated time as if it's a proper time.
The only philosophical question here is whether the thing measured by clocks is really time. If one adopts a notion of time as being something other than that, it's a purely philosophical notion of time that has no basis in physical reality.

Last edited: Nov 28, 2015
15. Nov 28, 2015

### MachPrincipe

I understand at last! Well, it is not proper time what they are talking about, but you can make the proper time enter into arena very easily: just allow the light signal to. bounce bacl to the origin and you are done. Even if it didn't take any time or very small time to make this path from tje POV of the Earth, still with the explanation of the video you are ahowwing the concept of time dilation. The more subtle problem of the simultaneity would be left to explaiin why the ship does not detect any assymetry in the two halves of the ray travel.

As for the time dilation being proved with just the light clock example, I do not buy it. I have no objection if you already have the Lorentz transformations. If you start just from the two principles and go straight to time dilation, I do not think that it is enough to demonstrate time dilation, you don't already know if the things will be coherent in all inertial reference systems and all directions. Just go back to Einstein derivation of time dilation. First the coordinate transformations. If not, you would need proving an infinite set of particular cases, and light clock with tranversal path is just one of them.

16. Nov 28, 2015

### Mister T

No, you will still have an amount of time that depends on the relative speed of the observer. Proper time is the time that elapses between two events that occur at the same place in some reference frame.

This follows from the definition $(\Delta \tau)^2=(\Delta t)^2-(\Delta x)^2$. Only when $\Delta x=0$ is the time $\Delta t$ equal to the proper time. It's value is the same regardless of the speed of the observer.

You do need to demonstrate that lengths perpendicular to the direction of motion are the same in both frames, and that is easy to do using just the first postulate. You also need isotropicity of space, but that is something you need in any proof of time dilation.

Last edited: Nov 28, 2015
17. Nov 28, 2015

### MachPrincipe

We don't understand each other here even if I believed that I got finally your point. My situation is: event 1, the light ray starts at one end of ship in direction to front end.Reaches the mirror, event 2 and it is reflected back to the starting point, arriving later, event 3. The time lapse between events 3 and 1 is a proper time, as they happen at x=0 of the ship coordinate system. As for the Earth. the coordinate time of events 3 and 1 is different, the coordinate time is not proper time as the x'1 and x'3 are different, and t'3-t'1 is greater than t3-t1, time dilaation. In the extreme example put in my post, you only need half a way to see the enormous differences of times of each inertial system.

Agree with that. But still ai am skeptical that you have proof of time dilation without going first through Lorentz transform. It could happen that you get time dilation in that scenario using only the principles but in another scenario you get a different expression for time diñation, i.e., a contradiction. So either you cover all spacetime with the gedanken experiments or you go first with the transformations of coordinates which ensures the self-consistence of the postulates being reconciliable each other in spite of its initial appearance.

18. Nov 28, 2015

### Mister T

Yes, you're right. I was thinking of the presentation in the video. The time measured by Earth observers is not a proper time. Sorry for not making that clear.

In that video they show that rocket particles have to travel a further distance than they would if the rocket weren't moving. That is true only for observers, like Earth observers, who observe the rocket in motion. Earth observers measure the time the particles have to travel, but that is not a proper time. In the video they imply that it is. You cannot make that a proper time by having the particles reflect and return to their original position relative to the rocket.

Last edited: Nov 28, 2015
19. Nov 29, 2015

### MachPrincipe

Surely the video explanation is wrong and messed up, but I got the concept. In fact, I always found the distinction among proper coordinates and coordinate coordinates (!) rather superfluous. You could do any calculation by using proper time alone, introducing later extra calculations. I did it so always when volunteering to the blackboard, to the dismay of teacher, but I insisted I would not use those misleading Lorentz transformations (I was young and rebel, then).

20. Dec 1, 2015

### phinds

Light speed is constant regardless of the motion of the source. Momentum/speed of the source is irrelevant. That is the very essence of Special Relativity.