What a pity EInstein didn’t write a sequel to Alice in Wonderland.

AL now: Well, I don’t think I missed it. I stated it. But let me state it again as simply as possible: You say that Houston can’t say that the clock below registers less time than the clock above for the reason that the time units it counts below are “longer in duration” than the ones counted by the clock above — so the clock below ticks more slowly. He is not allowed to say that that is the reason.

But the clock above records 1 hour say when the clock below records 1/2 hr. May I on behalf of all the oppressed hacks in the world, as well as all the chambermaids, all the taxi drivers, all the Aunt Sadies and even possibly all the Houstons of the world (I think) remark that this looks very like saying the clock below counts one while the one above counts two, and therefore the unit of time below being one-half-hour the unit of time above looks very like double the duration, at one hour, or two half-hours. ie one unit of time below seems to be longer by double than the one unit of time above, since both those durations clock the same above and below?

Now I instinctively sense that this is not Einsteinian, because it implies an absolute time clocked somewhere else, when all time is relative. I sense therefore that it should be more a matter of saying that the units of time are the same, but the ones below are twisted by the spatial distance between them in space-time into being equivalent to two of the ones above. How one imagines this works is beyond me because I am not a physicist who has worked with this stuff, but that appears to be to my dim perception to be what you are saying.

Even so, how can one possibly explain to me or the chambermaid or Houston (if he is saying the duration of units above and below is different, which I understand him to be saying, and Rossler to be saying too) that this simple view is wrong? The outcome is the same right?

I just don’t know how to explain it, and I thought you might. But the only explanation you are offering at the moment is that if what they say was true, then td=tu, which is obviously doesn’t.

Sorry about my verbose tautologies and parade of marching lockstep trivialities but you make the mistake of thinking I am arguing with you in some way, when I am merely following you panting and stumbling as you hop and skip up the mountain far ahead of me.

You shouldn’t be impatient with your students, TRMG, when they sit at your feet, laboriously taking notes, licking the pencil tip every few seconds, and then show you the notes and ask you whether they have it straight! :-)
.….….
TRMG on October 27, 2011 3:30 am: AL continued ““(1) The first equation is t_down = t_up/(1+z).
(2) The second equation is N_down = N_up/(1+z),
(3) Einstein’s Eq. (30a) is apparently t_down = t_up/(1+z) where z = Phi/c².
All three seem to be saying more or less the same thing.”

TRMG on October 27, 2011 3:30 am :Except that they don’t. (1,3) are statements about proper time, and are universally true in the Schwarzschild metric and the Rindler metric whereas (2) is a statement about numbers of time units and requires the auxiliary assumption that time gets measured in equal units to become true. Confusing both kind of statements is, in the present context, a potential minefield.”

AL now: There we are, just what I thought. But Alas, I have to ask, what is “proper time”? You mean time as opposed to space? You mean time as opposed to the incorrect Houston idea of time, as stretchable units? But I thought you just said that time units did NOT vary?? (first para above) Now you say time measured in equal units is needed to make the statement (2) The second equation is N_down = N_up/(1+z) true. You mean a false assumption is needed to make a false equation true? Or that a possible assumption is needed to make a possible equation true?

So are you saying that assumption is impossible and wrong, or that it can be made, if you like?

TRMG on October 27, 2011 3:30 am continued: AL: “You say Rossler accepts (2) as experimental fact but then wants to say his Eq. Rossler (1), T_down = T_up*(1+z), explains all, when in fact it contradicts Eq (1) t_down = t_up/(1+z). ”

TRMG on October 27, 2011 3:30 am:Yes, this is exactly what I am saying.”

AL now: Good.

TRMG on October 27, 2011 3:30 am continues: AL: “Houston seems to be saying that Eq. Rossler (1), T_down = T_up*(1+z) works because it means Time units down are longer than Time units up and therefore the count of them is fewer ie 999 seconds instead of 1000 in the same time period. So his T is the length of a time unit not the number of time units clocked.

You are saying that this doesn’t work, because time units are the same all over? That is a generally accepted premise in EInstein’s explication, is it not?”

TRMG on October 27, 2011 3:30 am: No, I say this doesn’t work because it is tantamount to absolute time: t_down = t_up, and thus violates Einstein’s t_down = t_up/(1+z). You just acknowledged that; now you apparently forgot it again. Very odd.”

AL now: Must be some misunderstanding here. I certainly acknowledge t_down does not equal t_up. The clocks show different times, Einstein tells us this. Then I understood you to be saying this was not because time units varied in length but because of Einstein’s theory that velocity or acceleration or position in space or space-time or some other outrage to common sense so dictates. And that this relation is expressed as t_down = t_up/(1+z).

OK so just say again, are time units the same all over this map or not? If they are and Houston is wrong to say they are of different duration up and down, then why can’t I say it, and believe that Einstein says it too? Or is Houston right after all?

TRMG on October 27, 2011 3:30 am continues: AL: “You finish by pointing out that if the time downstairs td = the number of units times the length of the units = Nd*Td
this is the same as saying
t_down = [N_up/(1+z)] *[T_up*(1+z)]
(because according to Rossler Eq. Rossler (1), Td = T_up*(1+z)
and according to your second equation Nd=Nup/1+z).
Fair enough.
That resolves into = Nu*Tu which resolves into tu. So time up equals time down, which contradicts Einstein.

You do seem to have presented Rossler with a certain difficulty here, unless he believes that time units downstairs are bigger than time units upstairs, as Houston holds. ”

TRMG on October 27, 2011 3:30 am: What? No. Not “unless,” but “because.” It is precisely this belief which causes the trouble. You just noticed that it played an essential role in the argument and even identifed the step in which it was used. Now you are suggesting that Rössler could somehow avert the conclusion, which contradicts Einstein, by assuming the very premise on which it was based? This makes no sense.”

What ?! I meant unless or because, as in if, ie unless or because or if he believes that time units downstairs are bigger or longer than time units upstairs. Which you now are saying again is wrong, right? Because that is “the belief which leads to trouble” etc.

So you are telling us that the time units are the same below and above, and the clocks tick off different times elapsed for some other reason.…

That is what I was checking.

But now I feel I have to check it again.

(2) The second equation is N_down = N_up/(1+z) is right, but only if units of time are not different in duration up and down?

And Houston and Rossler have it that time units are different up and down, and they cannot have their way, because it resolves to td=tu?

I write this out with all due respect TRMG, aware that you have a life, and may not have time to respond, but I hope I have made the thing clear, and have got it right, and that we have identified what you think is wrong about Houston and Rossler’s understanding, and that is the objection that Rossler has to deal with.

If you agree, then possibly you can also enlighten me as to where time slows to a standstill? And where it is infinitely fast?

I would imagine that

I am absolutely sure that we will see never

- a consistent and unequivocal definition of the Ts and their connection to the quantities in general relativity

- a consistent and clear answer to TRMGs reductio ad absurdum.

Instead Rössler will state again and again that no one can think. Except his blind followers of course.

There is the reductio ad absurdum of YOUR eq1. Disprove it or shut up!

That is the conclusion. I should add that this conclusion is not new but at least 3 years old.

You can not defend your wrong equations? :D

Why, of course. Accepting tentatively as true the statement you want to refute is the proper course of argument per reductio ad absurdum. So I assume that time units vary just as Rössler proposes, not because I think this is a true statement, but because I want to draw a conclusion from it which is (or should be) even more obvioulsy false, i.e. t_up = t_down. This was the fundamental point of the argument. How could you have missed that?

“Which is it? If the time on the clock downstairs is shorter ie fewer hours or minutes or seconds registered than the time registered on the clock upstairs in hours or whatever, and the duration of the units in the same in both places, then there must be fewer of them clocked downstairs than upstairs.”

Well, this is but a verbose tautology. The main-clause is already completely included in the if-clause. Did you really mean that?

“(1) The first equation is t_down = t_up/(1+z).
(2) The second equation is N_down = N_up/(1+z),
(3) Einstein’s Eq. (30a) is apparently t_down = t_up/(1+z) where z = Phi/c².
All three seem to be saying more or less the same thing.”

Except that they don’t. (1,3) are statements about proper time, and are universally true in the Schwarzschild metric and the Rindler metric whereas (2) is a statement about numbers of time units and requires the auxiliary assumption that time gets measured in equal units to become true. Confusing both kind of statements is, in the present context, a potential minefield.

“You say Rossler accepts (2) as experimental fact but then wants to say
his Eq. Rossler (1), T_down = T_up*(1+z), explains all, when in fact it contradicts Eq (1) t_down = t_up/(1+z). ”

Yes, this is exactly what I am saying.

“Houston seems to be saying that Eq. Rossler (1), T_down = T_up*(1+z) works because it means Time units down are longer than Time units up and therefore the count of them is fewer ie 999 seconds instead of 1000 in the same time period. So his T is the length of a time unit not the number of time units clocked.

You are saying that this doesn’t work, because time units are the same all over? That is a generally accepted premise in EInstein’s explication, is it not?”

No, I say this doesn’t work because it is tantamount to absolute time: t_down = t_up, and thus violates Einstein’s t_down = t_up/(1+z). You just acknowledged that; now you apparently forgot it again. Very odd.

“You finish by pointing out that if the time downstairs td = the number of units times the length of the units = Nd*Td
this is the same as saying
t_down = [N_up/(1+z)] *[T_up*(1+z)]
(because according to Rossler Eq. Rossler (1), Td = T_up*(1+z)
and according to your second equation Nd=Nup/1+z).
Fair enough.
That resolves into = Nu*Tu which resolves into tu. So time up equals time down, which contradicts Einstein.

You do seem to have presented Rossler with a certain difficulty here, unless he believes that time units downstairs are bigger than time units upstairs, as Houston holds. ”

What? No. Not “unless,” but “because.” It is precisely this belief which causes the trouble. You just noticed that it played an essential role in the argument and even identifed the step in which it was used. Now you are suggesting that Rössler could somehow avert the conclusion, which contradicts Einstein, by assuming the very premise on which it was based? This makes no sense.