Is time universal? NO (and its proof)

[Billy T]

This setup leads to a very interesting question, which I'm about to open another thread to address.

Your new thread is far too advanced for me (and I think all who post here). Why make a problem of SR into one of GR? Don't we have enough difficulty already?

 

[Neddy Bate]

This is truly amazing! I never realized SR time dilation was modeled like this! Thank you Pete, for taking the time to create this table. I find it very informative, and perhaps I might even be starting to understand.

</em>Firstly, here's the scenario with more detail. I've set it up so that the clocks are always at whole numbers when receipts are printed.

• Ten synchronized clocks are equally spaced 52 m apart on the embankment, labeled EA to EJ.
• Ten synchronized clocks are equally spaced 52 m apart on the train, labeled TA to TJ.
• The distance between embankment clocks in the embankment frame is equal to the distance between train clocks in the train frame.
• The train clocks are labeled in reverse order to the embankment clocks to make the problem easier for me (it makes it symmetrical).
• The first clocks to meet are EA and TA. They pass each other as EA reads 20 and TA reads 400.
• The relative speed of the train and the embankment is 86.6% of light speed, so that lengths are contracted by two and time is dilated by two.
• The unit of time is microseconds.

Here is a table of the receipts generated as each pair of clocks pass. The format is EmbankmentTime, TrainTime.
<table border=1 cellpadding=4 align=center><tr><td></td><td>EA</td><td>EB</td><td>EC</td><td>ED</td><td>EE</td><td>EF</td><td>EG</td><td>EH</td><td>EI</td><td>EJ</td></tr><tr><td>TA</td><td>20,400</td><td>22,401</td><td>24,402</td><td>26,403</td><td>28,404</td><td>30,405</td><td>32,406</td><td>34,407</td><td>36,408</td><td>38,409</td></tr><tr><td>TB</td><td>21,402</td><td>23,403</td><td>25,404</td><td>27,405</td><td>29,406</td><td>31,407</td><td>33,408</td><td>35,409</td><td>37,410</td><td>39,411</td></tr><tr><td>TC</td><td>22,404</td><td>24,405</td><td>26,406</td><td>28,407</td><td>30,408</td><td>32,409</td><td>34,410</td><td>36,411</td><td>38,412</td><td>40,413</td></tr><tr><td>TD</td><td>23,406</td><td>25,407</td><td>27,408</td><td>29,409</td><td>31,410</td><td>33,411</td><td>35,412</td><td>37,413</td><td>39,414</td><td>41,415</td></tr><tr><td>TE</td><td>24,408</td><td>26,409</td><td>28,410</td><td>30,411</td><td>32,412</td><td>34,413</td><td>36,414</td><td>38,415</td><td>40,416</td><td>42,417</td></tr><tr><td>TF</td><td>25,410</td><td>27,411</td><td>29,412</td><td>31,413</td><td>33,414</td><td>35,415</td><td>37,416</td><td>39,417</td><td>41,418</td><td>43,419</td></tr><tr><td>TG</td><td>26,412</td><td>28,413</td><td>30,414</td><td>32,415</td><td>34,416</td><td>36,417</td><td>38,418</td><td>40,419</td><td>42,420</td><td>44,421</td></tr><tr><td>TH</td><td>27,414</td><td>29,415</td><td>31,416</td><td>33,417</td><td>35,418</td><td>37,419</td><td>39,420</td><td>41,421</td><td>43,422</td><td>45,423</td></tr><tr><td>TI</td><td>28,416</td><td>30,417</td><td>32,418</td><td>34,419</td><td>36,420</td><td>38,421</td><td>40,422</td><td>42,423</td><td>44,424</td><td>46,425</td></tr><tr><td>TJ</td><td>29,418</td><td>31,419</td><td>33,420</td><td>35,421</td><td>37,422</td><td>39,423</td><td>41,424</td><td>43,425</td><td>45,426</td><td>47,427</td></tr></table>

It looks to me like the 'moving' clocks are ticking faster instead of slower. Did you use gamma or 1/gamma? Perhaps it is a by-product of length contraction? Or I might just be interpreting the frames backwards. Anyway, I will use these results to attempt to answer the following instructional questions.

</em>It will be difficult to make sense of this table, so take it slowly.
Here are some questions that might help:

• TA and EA are the first clocks to meet. What are the second pair of clocks to meet?
• Look a the EB,TD receipt. Did this meeting happen at the same time as EC,TB? Did it happen at the same time as ED,TC?
• Think about how you discover from the receipts (if possible) just how fast a particular clock is ticking in each frame.
• What else can the receipts tell you? Can they tell you how far apart any pair of clocks is at any time in each frame?

• The second pair of clocks to meet in frame E would be TB and EA, but the second pair of clocks to meet in frame T would be TA and EB.
• EB,TD happened at the same time as EC,TB only in frame E. EB,TD happened at the same time as ED,TC only in frame T.
• All clocks are ticking at one tick per second in their own frame, but they are ticking at two ticks per second in the 'other' frame.
• The receipts also tell us that a total of 27 seconds elapse (regardless of reference frame) while the block of 10 (A,B,C...J) train/embankment clocks pass by each other.

Hmm, that last line doesn't bode well for 'young-twin / old-twin' arguments based on SRT alone. There is already a receipt EJ,TJ that reads 47,427 so there is no reason to presume that if the train decelerated it's clock would revert back to 418, for example. What am I missing?

 

[Pete]

Your new thread is far too advanced for me (and I think all who post here). Why make a problem of SR into one of GR? Don't we have enough difficulty already?

It is difficult, but it doesn't have to be a GR problem since it doesn't need curved space - SR should be enough to solve it (although not necessarily easily!)

 

[Pete]

This is truly amazing! I never realized SR time dilation was modeled like this! Thank you Pete, for taking the time to create this table. I find it very informative, and perhaps I might even be starting to understand.

You're welcome, Neddy! I like to feel useful.

• All clocks are ticking at one tick per second in their own frame, but they are ticking at two ticks per second in the 'other' frame.

Are you sure about this?
Choose a clock. Any clock.
How do you tell how fast it's ticking?

• The receipts also tell us that a total of 27 seconds elapse (regardless of reference frame) while the block of 10 (A,B,C...J) train/embankment clocks pass by each other.

Hmm, that last line doesn't bode well for 'young-twin / old-twin' arguments based on SRT alone. There is already a receipt EJ,TJ that reads 47,427 so there is no reason to presume that if the train decelerated it's clock would revert back to 418, for example. What am I missing?

I'm not sure what you're getting at... When you say "it's clock", you mean clock TJ?
Why would it revert back?

 

[Neddy Bate]

EDIT: Just ignore this and use Pete's table. I was interpreting the frames opposite to what Pete intended, and this post is the result.

tI have rearranged the table so that the tick rate of clocks in the 'moving' frame is slower than the rate in the 'stationary' frame. My reasoning is based on the well-known light-clock explanation of SR. The light-clock ticks slower when it is in relative motion because of the longer path the light must travel. The path of the light in the relatively moving clock has horizontal and vertical components, yet the light in the relatively stationary clock has only a vertical component. Hence, the 'moving' clock ticks less often.

To avoid the need for ".5" decimals, the standard tick rate in a stationary frame is 2, while the standard tick rate in a moving frame is 1. This might require Pete to change his distance between the clocks, but I am leaving that distance unspecified, except to say that the spacing is identical in both rest frames. All clocks are identically constructed. Within their own rest frames, the clocks are synchronized to read the same reading on all clocks at any given moment in time -- (perception delays are duly factored out, not neglected). For now, we need not specify any units for clock readings.

I have also made some other changes that allow me to visualize this more easily. I hope that having two different tables will not cause confusion in this thread. If my table is shown to be wrong or problematic, I am willing to delete this post.

As before, the embankment frame is E, the train frame is T, and the clocks are lettered A-J. The first clocks to meet: clock "E,A" (which reads 20) and clock "A,T" (which reads 400). The format of the printed readings is "20,400". I find this notation unambiguous, and easy to read.

<table border=1 cellpadding=4 align=center><tr><td></td><td>E,A</td><td>E,B</td><td>E,C</td><td>E,D</td><td>E,E</td><td>E,F</td><td>E,G</td><td>E,H</td><td>E,I</td><td>E,J</td></tr><tr><td>A,T</td><td>20,400</td><td>21,402</td><td>22,404</td><td>23,406</td><td>24,408</td><td>25,410</td><td>26,412</td><td>27,414</td><td>28,416</td><td>29,418</td></tr><tr><td>B,T</td><td>22,401</td><td>23,403</td><td>24,405</td><td>25,407</td><td>26,409</td><td>27,411</td><td>28,413</td><td>29,415</td><td>30,417</td><td>31,419</td></tr><tr><td>C,T</td><td>24,402</td><td>25,404</td><td>26,406</td><td>27,408</td><td>28,410</td><td>29,412</td><td>30,414</td><td>31,416</td><td>32,418</td><td>33,420</td></tr><tr><td>D,T</td><td>26,403</td><td>27,405</td><td>28,407</td><td>29,409</td><td>30,411</td><td>31,413</td><td>32,415</td><td>33,417</td><td>34,419</td><td>35,421</td></tr><tr><td>E,T</td><td>28,404</td><td>29,406</td><td>30,408</td><td>31,410</td><td>32,412</td><td>33,414</td><td>35,416</td><td>35,418</td><td>36,420</td><td>37,422</td></tr><tr><td>F,T</td><td>30,405</td><td>31,407</td><td>32,409</td><td>33,411</td><td>34,413</td><td>35,415</td><td>36,417</td><td>37,419</td><td>38,421</td><td>39,423</td></tr><tr><td>G,T</td><td>32,406</td><td>33,408</td><td>34,410</td><td>35,412</td><td>36,414</td><td>37,416</td><td>38,418</td><td>39,420</td><td>40,422</td><td>41,424</td></tr><tr><td>H,T</td><td>34,407</td><td>35,409</td><td>36,411</td><td>37,413</td><td>38,415</td><td>39,417</td><td>40,419</td><td>41,421</td><td>42,423</td><td>43,425</td></tr><tr><td>I,T</td><td>36,408</td><td>37,410</td><td>38,412</td><td>39,414</td><td>40,416</td><td>41,418</td><td>42,420</td><td>43,422</td><td>44,424</td><td>45,426</td></tr><tr><td>J,T</td><td>38,409</td><td>39,411</td><td>40,413</td><td>41,415</td><td>42,417</td><td>43,419</td><td>44,421</td><td>45,423</td><td>46,425</td><td>47,427</td></tr></table>

EDIT: The following two paragraphs neglected the fact that clocks can only be synchronized in one reference frame at a time.

Consider clock E,A in the reference frame of E. The rate of this clock is the 'standard' rate of 2 units (20, 22, 24...). As the train clocks A,T through J,T pass by this point in frame E, they are ticking at 1 unit, or half of the standard tick rate (400, 401, 402...).

Also consider clock A,T in the reference frame of T. The rate of this clock is the 'standard' rate of 2 units (400, 402, 404...). As the embankment clocks E,A through E,J pass by this point in frame T, they are, likewise, ticking at 1 unit, or half of the standard tick rate (20, 21, 22...).

I would prefer to have a consensus on this before proceeding to some of the questions/problems I have regarding this system, and also before proceeding to the cases of acceleration, etc. which are beginning to unfold in the other thread.

 

[Pete]

Consider clock E,A in the reference frame of E. The rate of this clock is the 'standard' rate of 2 units (20, 22, 24...). As the train clocks A,T through J,T pass by this point in frame E, they are ticking at 1 unit, or half of the standard tick rate (400, 401, 402...).

Also consider clock A,T in the reference frame of T. The rate of this clock is the 'standard' rate of 2 units (400, 402, 404...). As the embankment clocks E,A through E,J pass by this point in frame T, they are, likewise, ticking at 1 unit, or half of the standard tick rate (20, 21, 22...).

Careful Neddy, you're making a common mistake.

What is the tick rate of clock AT in the embankment frame? Step me through how you calculate that rate from the receipts.

Key point:
In the embankment frame, the time on clock BT is not a reliable indicator of the time on clock AT.

 

[Billy T]

I too thank Pete. Once again he has shown exceptional willingness to provide numerical data for us to chew upon.

...It looks to me like the 'moving' clocks are ticking faster instead of slower.....

Interesting that we don't agree on this even though we are looking at the same table. Let me explain how I think:

Assume I am on the train and I want to know how fast are the embankment clocks ticking (Recall all my clocks show the same time simultaneously, so in the first column of Pete's table I find that at the initial meeting of clocks my clocks all showed 400 and that clock E,A showed 20. 18 seconds later for me on train my clock next to clock E,A showed it had advanced only 9 seconds - For us "train riders", it is clear that embankment clock E,A is running slow. (It could be that they were not sychronized, but my twin brother on the ground assures me they were, so I assume that all of them were for them showing 29 at their silly idea of "simultaneous")

Now see what my twin brother standing on the ground wired me:
He said (using the clock E,A and the row of data about what all of my clocks were showing): that when all of the embankment clocks were showing 22 one E,B) was next to train clock T,A and that train clock was showing 401 -I.e. despite two seconds had passed on the ground, the train clocks were only showing one second had past! - The train clocks were running slower. just to be sure He double checked: When all of the embankment clocks were showing 38 the embankment clock happed top print 38 on the same paper that a train clock printed 409 (does not matter which train clock it was - all the train clocks were then (simultaneous on the train) showing 409.

Thus MacM's "physical impossibility" was happening! All of the train clocks were ticking at half the rate of the embankment clock and all of the embankment clocks were accumulating only half as many ticks as the train! that is in two minutes on the train (120 one second ticks) the embankment clocks only ticked 60 times. Yet on the ground the same identical clocks ticked 120 times while those on the train ticked on 60 times!

MacM's "mutual reciprocity" is not as impossible as it appears intuitively to be (the naive view). It is completely possible, in fact true.

 

[DaleSpam]

MacM's "mutual reciprocity" is not as impossible as it appears intuitively to be (the naive view). It is completely possible, in fact true.

Woah! That sent my head spinning so fast that time contracted and distances dilated.

-Dale

 

[Pete]

Hi Billy,
Thanks for taking the time to work through it.

 

[Raphael]

@Pete

You have an discrepancy between your scenario and your data.

One of these conditions is not supported by the data given:

• The relative speed of the train and the embankment is 86.6% of light speed, so that lengths are contracted by two and time is dilated by two.
• The unit of time is microseconds.

Or, the distances between clocks (in the clocks' rest frame) are not accurate.

 

[MacM]

Thus MacM's "physical impossibility" was happening! All of the train clocks were ticking at half the rate of the embankment clock and all of the embankment clocks were accumulating only half as many ticks as the train! that is in two minutes on the train (120 one second ticks) the embankment clocks only ticked 60 times. Yet on the ground the same identical clocks ticked 120 times while those on the train ticked on 60 times!

MacM's "mutual reciprocity" is not as impossible as it appears intuitively to be (the naive view). It is completely possible, in fact true.

You are a bit to quick to make any claims.

This table disregards emperical data and only seems SR valid because you also assume length contraction; which doesn't happen if you don't disregard the dilated tick rate of the train clock.

Try again.


PETE:

You stated tick rate was 0.5 and length is 0.5.

Did you apply SRT's condition of relative velocity equally to both frames.


From the trains POV it is the embankment that has motion.

 

[Pete]

Mac,
The purpose of the table is to illustrate the predictions of SR in that particular situation. You are welcome to maintain that it is not what would happen in reality if that's what you want.

 

[Pete]

@Pete

You have an discrepancy between your scenario and your data.

One of these conditions is not supported by the data given:

• The relative speed of the train and the embankment is 86.6% of light speed, so that lengths are contracted by two and time is dilated by two.
• The unit of time is microseconds.

Or, the distances between clocks (in the clocks' rest frame) are not accurate.

Thanks for checking my figures, Raphael.
I do believe you're right - I think I should have set the distance between the clocks should be 520m, not 52m.

 

[MacM]

Mac,
The purpose of the table is to illustrate the predictions of SR in that particular situation. You are welcome to maintain that it is not what would happen in reality if that's what you want.

I do indeed but I was responding to Billy T's claim that the Table demonstrates the validity of SRT. My question was to show that it does not include all SR predictions.

QUESTION:

1 - Does your table include time dilation from the embankment view and spatial contraction from the train view.?

2 - Does your table include time dilation from the train view and spatial contraction from the embankment view.?

3 - Why would you find it irrelevant that spatial contraction is a view based on the assumption that ones clock tick rate are standard. The fact that the emperical data shows (at least the clock in motion - having accelerated) does tick slower than the rest clock means distance didn't actually change. Distance in SRT is a function of d = vt but 't' is ticking slower, therefore no physical distance changed. My question was did you actually reduce distance when computing clock meetings?

Because if you did your timings will be off. If you didn't then you didn't follow SRT.

 

[Pete]

Hi Mac,
You can answer those questions by examining the table and the initial conditions.
What do the numbers tell you?

 

[MacM]

Hi Mac,
You can answer those questions by examining the table and the initial conditions.
What do the numbers tell you?

They tell me SRT is bogus.

Now for other readers how about answering the questions so we can put Billy T's comments on ice.

 

[Pete]

Really?
You can't look at the numbers and tell me how far apart the train clocks are in the embankment frame and how fast they're ticking? And vice versa?

I don't think you've even tried.

Something else for you to consider:

Can you look at the numbers and tell which frame is moving and which is not?

 

[MacM]

Really?
You can't look at the numbers and tell me how far apart the train clocks are in the embankment frame and how fast they're ticking? And vice versa?

I don't think you've even tried.

Frankly I did look at the numbers. You said 52m. Way off. You have now corrected that to be 520m.

0.866c * 3E⁸m/s = 2.598E⁸m/s *times 2E^-6seconds = 519.6m (close enough)

Something else for you to consider:

Can you look at the numbers and tell which frame is moving and which is not?

Of course not. But answer this. Before the train began its motion the observers measure 520m between clocks both on the train and on the embankment.

Now with the train whizzing by and taking 2us between clock intersections notes that the embankment clocks have only ticked 1us. From that you want to claim that the distance between embankment clocks is now only 260m.

Ditto for the embankment observers view of the train clocks and spacing.

If the above were physical fact then there would be no dilated time on clocks after the test. Since emperical data demonstrates that clocks do dilate if given accelerated motion and there is no emperical data to support the claim that the embankment clocks would be dilated, suggests that you are double counting a physical affect claiming spatial contraction when it does not exist just to justify SRT.

I agree that is the prediction. Job well done BTW on the table. However, my point to Billy T is that does not make it so. It only shows you can put the prediction down on paper. It does not prove it is reality.

In fact data demonstrates it is not. That was my only point.

Also to point out that this is different than has been claimed here by others. It has been claimed that time dilation is in one frame and spatial contraction is in the other. Yet your table shows that both affects are being claimed by one frame.

i.e. - The train claims time dilation of embankment clocks and also concludes the embankment spacing is 260m. Ditto for the embankment view of train clocks and spacings.

If spatial contraction were a fact then no clock would ever be dilated after the test.

 

[Pete]

Now with the train whizzing by and taking 2us between clock intersections notes that the embankment clocks have only ticked 1us. From that you want to claim that the distance between embankment clocks is now only 260m.

Ditto for the embankment observers view of the train clocks and spacing.

Look at the data - from the data, you can determine the distance between moving clocks without making any assumptions about time dilation.

Here's an example:
On the embankment, we find the distance between two train clocks by noting where they are at some instant. For example, at t=34&mu;s, TA is at EH, TJ is half way between EC and ED, and the rest are spaced evenly in between.
The space between train clocks is clearly half the space between embankment clocks.

Likewise, time dilation can also be directly observed in the data without any assumptions about length contraction.

And yes, in both frames the moving clocks tick slower and are closer together, and this is as predicted by special relativity.

 

[Billy T]

....I agree that is the prediction. Job well done BTW on the table. However, my point to Billy T is that does not make it so. It only shows you can put the prediction down on paper. It does not prove it is reality. In fact data demonstrates it is not. That was my only point.
...

...MacM's "mutual reciprocity" is not as impossible as it appears intuitively to be (the naive view). It is completely possible, in fact true. ...

To MacM:
I must be allowed to express my opinion also (the last three words above), if you can.

The main point of my comments reposted above is that clearly "reciprocity" is possible - I.e. that your often repeated opinion that SRT's "reciprocity" is "obviously impossible," "physical impossibility" "nonsense" etc. is disproven by Pete's hard work / table.

I agree that calculations showing that it is possible (and that your claims to the contrary are false) does not prove this is what is in fact true in reality.

However you must now admit that "reciprocity is impossible," "nonsense," "obviously false" "etc." is not a disproof of SRT also.

I grant that it is "naively obviously" that that the clocks in two different frames can not both be ticking slower than the one in the other frame, IF ONE DOES NOT WORRY ABOUT HOW TICK RATES ARE TO BE MEASURED.

I have tried many time to get you to stop simly asserting the naive view that there is no problem with "simultanity" or to recognize that to measure "tick rates" one must have a "start event" and a "stop event" between which the number of ticks is counted.

I have (in the very first post of this thread) shown that observers in both frames can have the "start event" co-located and thus agree that it is simultaneous (I used explosions at end of the train and had both ground and train observers set t = 0 on thier clocks, thru their entire frames, when that explosion occurred.) However, they will never agree that the other observer used a "stop event" that was simultaneous with their own. (I did not use any SRT equations or permit any signal delays, or other "perception problems" etc. while proving this in first post of this thread.)

You consistently refuse to admit that there is any "simultyanity problem". You make statements like "tick rate is tick rate" etc.and refuse to recongize that there must be a "start event" and a "stop event" between which the number of ticks are counted. You either don't or won't understand that "simultanity" comes in because, althought the two different frame observers can agree on one (the start event is easier) event that both think the other used an incorrect "stop event" - I.e. did not stop counting ticks at the same (simultaneously") time as they did.