# You may see a light wave as relative time, without Lorenz time dilation calculated

1. Dec 1, 2011

2. Dec 2, 2011

### Simon Bridge

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

No proofs there.

3. Dec 2, 2011

### digi99

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

That topic is so long that most people don't read it anymore (misundertanding, than not, not easy readable anymore) understandable you have to spread your time. But I was right there in some parts (not the absolute points of course).

But short:

- I was calculating there a time dilation in frame A for B in frame B compared to a light wave, formula time dilation (lesser time) = V/C (or t' = t. (1 - V/C) or x' = x . (1 - V/C)) (I considered your own movement V. t is subtracted from the same light wave in frame A and B, the end effect is it will be smaller for B and distances too of course).

- after Lorentz is t' = γ . t . (1 - V/C) or x' = γ . x . (1 - V/C) (also described as x' = γ . ( x - V. t) or t' = γ . (t - V.x/C2)

- the time dilation calculated by A is a factor γ bigger after Lorentz as part of the calculation, as well t as V/C are corrected

- V/C seen in time is exactly the part V.t of the light wave in distance, so it looks you skipped time (V/C or V.t in distance of the total passsing length of the light wave)

- after Lorentz both parts are multiplied with γ but the effect is t' = t. 1/γ for B itselves (time dilation already invloved)

- for every other point in frame B is the same (V.t is subtracted from the light wave)

- thoughts are exactly the same as for a passing train (in 1 direction only, the driving direction)

- in thoughts is it now easier to see time dilation in mind, a light wave presents relative time and can be seen as a clock between two events, in our normal calculations of distances/time we don't consider the skipping part in relative time during the movement itselves (absolute time does not exists)

So your own movement compared with the light wave is V.t in frame A (or V/C in time dilation), after Lorentz in frame B γ . V.t (total length light wave smaller) and γ . V/C time dilation.

So the skipped part of a passing light wave gives the time dilation.

Now is the question what is the meaning of the time dilation calculated in frame A, it seems not the really time dilation (but the responceable part is proofed), therefore you need Lorentz.

Or maybe you don't need Lorentz and this is the time dilation (V/C), in that case V > C is possible. Maybe there are experiments where the time dilation is exactly meassured (so not just a time dilation) and confirmed Lorentz is absolutely right (CERN do your best).

First I thought now I can calculate it in another form (γ included without Lorentz, but after many many hours I gave up, impossible, too few facts).

4. Dec 2, 2011

### Staff: Mentor

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

digi99, I am sorry, I have tried multiple times now, but I cannot decipher your "proof" nor this explanation of your proof. I don't know what you are trying to prove, what your initial assumptions or starting formulas are, nor can I follow your derivation.

It is possible that you never had a class that required you to write formal proofs. I would recommend that you spend some time at this site http://zimmer.csufresno.edu/~larryc/proofs/proofs.html to get some good tips on how to organize your thoughts so that other people can follow your proof and be convinced by your logic.

Also, it is considered spam to post the same post multiple times. You should pick the one place where you think it fits best, not spam the forum. Linking to it from other places is OK if you want.

5. Dec 3, 2011

### Simon Bridge

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

I'm guessing that part of the problem we have understanding you is that English is not your first language.

I don't know what you mean by "lesser time".

I don't know what V/C is supposed to be - perhaps the relative speed divided by the speed of light?

t'=t(1-V/C) looks like it is supposed to be the time-dilation formula - in which case it should look more like this: $t'=t \sqrt{1-v^2/c^2}$ - is that what you meant? (If you quote me you'll see how I did that - it will help you a lot to learn to use LaTeX.)

The bit about light waves is a mystery because you have not explained which light wave and what it is doing there. The traditional derivation for time dilation uses a light-beam - is this what you are referring to?

None of the observers need to do any calculations to get the time dilation - all they have to do is look at each other's clocks.

... and so it goes.

You see - to make a "proof" you have to be very clear about everything you say. Otherwise it just looks like you have become confused.

6. Dec 3, 2011

### digi99

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

Thanks DaleSpam and Simon, I shall do my best not to spam anymore (unless the name DaleSpam). In fact I considered later that I came to the same things as in the very beginning of my first topic (in this forum) about light waves. It is for me also difficult to understand that many of you don't see what I mean in my topic. I had the same problems already in another forum, so there I stopped already (in my own language). I will do it now in a slow unspammed way, no hurry anymore. The spam is, I wanted to complete the topics, because many topics and all half answered/solved does not help either. But maybe can it be solved what is wrong. If no, no problem at all and let it rest. My answers are only to give views to physicists, maybe it leads to something (not for me because I have now to less knowledge). I must learn a lot in a short time, because I don't need to know all, my interest is only relativity and light for this moment.

I am a starter in relativity (mathematics background, a long time ago, but I have of course not learn the language of physicists and English is not my first language) , but I will take gass back because it takes too much time of my own work (independent). I read some books about Brian Green later. That was the reason that I wanted first to understand the basics of relativity because many books tells only a part of it (e.g. they don't start with the behaviour of light, so that was an immediately problem for me with my exact thinking, so did I come to my first topic in a physicist forum to get a view of light).

I think totally I gave enough information, but I know I got very few feedback (only from Ghwellsjr but ended in a kind of doppler effect what I did not mean).

It's for me (mathematics thinking) a big question you don't see the relation t'=t(1-V/C) (before Lorentz) and after Lorentz t'=γ.t(1-V/C). I tried to explain how I come to t'=t(1-V/C) by thinking in the Newton way.

I think Simon has not seen my drawing in answer #11 of the related topic as first in this topic meant (was a topic with a bad start, yes my first). If you have seen that (Simon), I think you understand how I came to that formula (what it means).

My thinkings were let's show a light wave (the same light wave in fact) in as well frame A (object A in rest, moving object B) and frame B (object B in rest). Because light has lead to time dilation and interesting subjects in relativity, whithout the secrets of light there was not been a very well known Einstein I guess.

(object A and B are persons now) So a light wave starts in frame A (x = 0) and a person B is moving at the same time. Person A may meassure what the speed is of person B in it's frame, and that is speed V. But person A thought I use the light wave as a clock to meassure the speed of person B (consider it now as thought experiment otherwise you will see Dopller effect, and better is to see person B on the y-axes and the light wave in the middle on that y-axes between person A and B). So A meassured the total length of the moving light wave (speed C) during time t (normally meassured with a normal clock) and recalculated the time used by dividing that length / C. That time is t too of course, but as in Newton you have to subtract your own movement (V.t) from that total meassured length of the passing light wave, so recalculated t_seen_from_a_for_B = t(1-V/C), t is here the conventional method with a normal clock or from the light wave (without subtracting B's own movement in frame A).

So A thought already, B must undergo a time dilation by calculation (A meassured t), but for B it must be t(1-V/C) (see drawing in #14).

After Lorentz for B, it's t' = γ . t . (1-V/C).

What is the relation. I conclude you may see a passing light wave as relative time (it is passing A), if you move you skip a part of that light wave (seen by B) and so B's time will be lesser at the same time A's it sees (logically because B skips a part of the light clock used, that's the light wave).

You must understand now what I mean ... there is only a factor γ more after the Lorentz transformation. The consequences are that B sees a smaller lightwave (compared to A) where it's total passing length (compared to A) is γ . V . t smaller or γ . V/C in time lesser (of course near γ . t). So the part of the skipped piece of passing light wave is responceable for the time dilation in B (at the same time compared with A time goes slower for B).

But I still don't know (unclear books) if it affects B's age ... (without twin paradox conditions) ...

Last edited: Dec 3, 2011
7. Dec 4, 2011

### digi99

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

Maybe is my explanation not clear enough (for Simon / DaleSpam), I turned my computer on.

A and B are comparing both times in a specific period by meassuring a passing light wave while both in rest (and uses the same light wave).

That's t for A and t' for B, but A tried to predict the time for B and saw already in it's prediction a time dilation V/C (he did not know that later a factor γ would be involved more because of Lorentz).

In fact what I want to say for a passing light wave is the same as for a normal clock, if you move a normal clock time goes slower but that is more difficult to see.

That's why I take a light wave in this example, generally I may say, a passing light wave presents (relative) time, (absolute time does not exist) like a clock (light is also used as a clock), if you move (compare with a train) you see lesser light passing. The final effect is you will see a smaller light wave (while you are moving at the same time the light wave is going smaller, but if you compare it to the size A it sees, in that size sees A already a time dilation for B).

Confused, I am not, but it is slowly a very difficult and heavy task for me to explain ... so difficult I would never expect before I started it with university people (I see it as very simple) ... next time with something else I let to read it first to others before placing it in a forum ....

Last edited: Dec 4, 2011
8. Dec 4, 2011

### digi99

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

This was in first instance a thought of me, but because I "proofed as a starter" you see the same time dilation (without factor γ) in the Lorentz formula, I think partly it can be true (but without the factor γ). So the question is, what meaning has that time dilation that A calculated in it's own frame ?

9. Dec 4, 2011

### ghwellsjr

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

Digi99 is trying to provide a simple way to illustrate time dilation which simply means a clock running slower the faster an observer moves. If you look at posts #1 and #6 on his link on the first post of this thread you will see the clearest explanation. He starts with a monochrome light source and two observers who have "special clocks" that can count the wave cycles of the light coming from the light source during a period of one second. The first observer's "special clock" counts out the same number of cycles as the light source is emitting in one second which he calls t. The second observer is moving at speed v away from the light source. He will count t(1-v/c) cycles coming from the light source. Thus, a very simple way to show that a moving observer's "special clock" runs slower than a stationary observer's "special clock". Note that at v=0 the "special clock" runs at the regular rate. At v=c the "special clock" comes to a standstill.

10. Dec 4, 2011

### digi99

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

Fantastic Ghwellsjr (thank you, a big relief), it is exactly what I meant. But it is only a partially explanation because the factor γ has to be found too in this way.

In fact I was trying to make Lorentz visible in a simple way with my topic. I had the thought (for to explain it simple to others) see passing light waves as the time, if you move you see lesser light waves passing so time goes slower. And that's a fact now (in fact simple because light is a exact clock for relative time, t(1-V/C) is visible as explained and in Lorentz). The same is valid for another type of clock but more difficult to understand/make visible.

I bought the books Brian Green and Sander Bias and was starting with professor Sander Bias, but I stopped because my problems with light.

So I did come to my topic while thinking about it. Now I was looking again in his book how he found the Lorentz formula in his time space diagrams (learned from that book in the start chapters) because I could not. And he is doing it in the exact way I was thinking, also in his book he works with the relative speed V/C and finds γ in that way. A very good book to understand relativity, all explained in detailed space time diagrams.

So this is a very good day for me. I can stop now with spamming and read the books slowly in the coming weeks, I am fully prepared now and shall read them more easily.

11. Dec 4, 2011

### Staff: Mentor

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

OK, this formula is incorrect. The correct formula is $t'=\gamma(t-vx/c^2)$. See here.

Where did this formula come from come from?

For clarity, let's introduce the following notation. Let all primed quantities refer to quantities measured in B's frame and let all unprimed quantities refer to quantities in A's frame. Let's use subscripts a, b, and c to refer to the coordinates of A, B, and the light pulse. Finally, let's denote the relative velocity of the frames by an unsubscripted v. So $v_a'=-v_b=v$ and $v_b'=v_a=0$ and $v_c=v_c'=c$.

12. Dec 4, 2011

### digi99

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

I am happy you asked this because I was on the last moment so confused with the derivations in my first topic (some are right, some are not right) I was not sure anymore and you forced me now to clarify the last things. Gladly it still fits. It took a few hours (a lot a papers).

The expression t(1-V/C) and x(1-V/C) are for the meassured light wave length (passing light wave) in frame A (how A it sees/calculated for B). So x is positioned on the light line and time t.

In frame B you must take the coordinates of the transformed light line and so you must take t' and x'. Lorentz : x' = γ . (x - v.t) = γ . (x - v/c . t . c) = γ . (x - v/c . x) = γ . x . (1 - v/c). And t' = γ . t . (1 - v/c). Pfff....

13. Dec 4, 2011

### Staff: Mentor

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

OK, so since you are describing the light then using the notation I described above this should be written: $t'_c=\gamma t_c(1-v/c)$ which can be derived from the Lorentz transform as follows
By the second postulate $t_c c=x_c$
By the Lorentz transform for the light wave $t_c'=\gamma(t_c-vx_c/c^2)$
So by substitution $t_c'=\gamma(t_c-v(t_c c)/c^2) = \gamma t_c(1-v/c)$

Huh? Please use the notation I suggested, or propose your own clear notation and I will use it. But I cannot tell if you intend these to be general coordinate transformations or if they are the coordinates of some specific worldline such as the worldline of the light pulse.

Last edited: Dec 4, 2011
14. Dec 5, 2011

### digi99

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

Hi DaleSpam, I take only conclusions by analysing so I learn from you and others. So what you wrote here is what I suggested (you did it in the right way). Tc is the same time for the moving object.

So from now on you can explain time dilation in a very simple way everybody in the world could understand, no magic anymore with complex drawings.

If you see a passing light wave as (relative) time, if you move, the light wave is slower passing you so time is going slower (time dilation). You have to compare it to the original size of the light wave when standing still, the finally effect will be when moving that the light wave you see wil being smaller, just as time do. It relates to the counting cycles of a light wave (the total length of the passing light wave).

I hope that I have added something extra to physics, I am sure this helps by analysing further by thinking lesser complex concerning time dilation.

Is it now allowed to place links to this topic to complete my other topics (last time), maybe there could be a new option in the future in this forum that you can update a topic without to place it as first in the queu of answers ?

15. Dec 5, 2011

### Simon Bridge

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

OK - so walk me through the process of getting the time dilation from a light wave?
Do I need a special light source or can I pick any of the normal environmental ones (Sun, moon stars)?

Um - no: light waves pass me just as fast when I move as when I don't.
I see fewer waves per second if I head away from the light source (doppler shift) but is it me that is moving or the light source? How do I tell?

16. Dec 5, 2011

### Staff: Mentor

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

In my notation $t_c$ is the time of an arbitrary event on the worldline of the light pulse in A's reference frame.

Sure, if you are willing to accept the Lorentz transform then time dilation is very simple and doesn't require any drawings to explain.

No, $v_c=v_c'=c$. The light wave passes at the same speed in every frame

This is the first mention here about counting cycles. I thought we were describing a brief pulse of light. If you are talking about a continuous source of coherent light, then is this source at rest in A's frame or B's frame?

We will need to modify our notation. I suggest that we replace the subscript c with a subscript number indicating which cycle of the light wave is referenced.

17. Dec 5, 2011

### ghwellsjr

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

18. Dec 5, 2011

### Staff: Mentor

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

If he is counting wave cycles then it sounds like Doppler shift, not time dilation.

19. Dec 5, 2011

### ghwellsjr

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

That's what I told him and that's what Simon Bridge told him, although it's not normal Doppler because he's basing the time duration on the stationary frame instead of the moving observer's frame.

I even pointed out that if the moving observer changes direction and returns to the stationary observer, both their "special clocks" will end up with the same "time" on them instead of what should be happening according to the Twin Paradox.

But he still thinks its a better way to illustrate time dilation even though he realizes that it only "works" in one direction and even though it only "works" correctly at v=0 and v=c.

20. Dec 5, 2011

### digi99

Re: You may see a light wave as relative time, without Lorenz time dilation calculate

I am very surprised we still are not agreed.

I am looking just to the found formulas, there is no doubt I guess they are right. Pure Lorentz but expressed in total length of the passing light waves and related time you did not seen before I guess, the same time as the time for the moving object but calculated in another way but with the same result (in fact I am not counting periods, that's a practice problem maybe, but I considered only the length of the passed light signal, do it in mind please, people you explain don't think in frequencies, cycles etc. only students at universities). But at the same time, that passing light signal is getting smaller because of the limitation C. So yes, the speed is always C, so you have to see in mind that light is going slower for a little moment and immediately because of that is going smaller (everything is going smaller, the total length and the periods if you like, the difference is because of the time dilation. Formulas don't lie otherwise I could not say this.

You see this all I think too difficult maybe you studied physics. But you have to think like average people. And the formulas are right, so I don't tell nonsence and it has nothing to do with Doppler (see the light waves on a distance). What I tell you is not important, look only to the formulas.

For me is time the same term like distance. Nature says distance / time = lightspeed C all times.

So take a ruler and consider that as time (exactly the same as for distance).

Let's move that ruler by another person (with eg. seconds drawned on it) in front of your eyes. Than you see time passing IN MIND (like with light). If you move (with light direction is not important, in both directions you should experience same effects because of the limitation C) that ruler is a little bit going slower really, because it cannot be going slower (C) it's by nature immediately corrected and the ruler is going shorter (IN MIND). The same for light waves, what is the problem ? You can make a machine for students with sensors in the ground, when they walk with your simulated light waves they will go smaller.

This you see in formulas at both sides. Before Lorentz you see a light wave which length expresses time (same time A sees in his frame for B). After Lorentz that piece of light wave is going smaller and so does time with factor 1/γ, this time experiences B (but not aware of). DaleSpam, this is not the example of the pulse problem just light, that I discuss in that topic. You see before Lorentz you can think in the newton way, see light as an object and subtract your own movement as you normally do. That is translated in the formulas (but a factor γ more). The speed of the light waves before and after Lorentz are still C at any moment (before Lorentz the total length of light waves is shorter because of B's movement, but it's time too, so still speed C).

If I am wrong (that's possible), than the formulas are wrong (but I don't believe)!

What is nice to this view, you can see light as an object and at the same time it is a clock.

By the way I thought today, if V could not be greater C, than there is nothing special about light, maybe because of his mass 0, it can have the highest speed possible detemined by nature. That's not a secret of light but from nature (there is probably one object with mass 0). If V could be grreater C, than the secret lies in light (time). So as long is not proofed V > C, I don't think anymore about that secret (not that I would found anything in other dimensions etc. but is not worth the time).

Last edited: Dec 5, 2011