I agree with much of what you have to say, but will adda few corrections/comments
reilly said:
Billy T -- Interesting, but not new. The National Bureau of Standards uses an atomic clock to define a second as so many cycles of emitted light- if I recall correctly, the clock is a cesium atom. So, for most of us, time is indeed measured as a series of events, but in princple, two would do. As Einstein pointed out, time is what we measure with clocks.
Several times I have noted that I am not stating any thng new and probably not even the first to give this proof. Cesium was an earlier version. (Rubidium now I think.) The second is defined by about 12 atomic clocks. (The one at the Applied Physics Lab of JHU, where I worked for almost 30 years contributed a few percent - don't know if it still exist and does - Retired more than 10 years ago.)
One of Einstein's major accomplishment was to show that clocks in different frames indicated different amount of time lapse between the same two events. He knew full well that the interval between two events was not any definite thing. (Not 5 seconds, not 10 seconds, nor any other number of seconds.) Others have already pointed out in this thread that he and his friend, Goedel, questioned the existence of time. You must be putting words in Einstein's mouth. Please give a reference to where and when he said what you claim he did.
reilly said:
...Your mathematics. First, it does not prove the nonexistence of time in any mathematical sense. To do so, you would have to find a contradiction in the usual mathematical use of time in physics. With your scheme, I can always map back to normal physicist's time.
I only claim that the math shows time is not required for a complete discription of the universe. Here you are putting words in my mouth. I infer that time does not exist because of this and two other facts, given in recent post when Tournesol erroneously accusted me of the same claim (Time is not observable and causes nothing.) I admit the title of this thread is a little misleading. It should have been: "Time Does Not Exist - An Opinion, Supported by Math Showing Time is not Required to Describe Universe" but there are space limitations.
reilly said:
...In your argument about removing time, you obviously must deal with functions that have an inverse, and as far as describing events that's a fairly restrictive constraint.
Very good point. I have been expecting it for a long time, as the existence of the inverse function is essential to my proof. You seem to know something about "conformal mapping" and that not all transforms are one-to-one mapping. In the first post of this thread I noted that I was using example A = 15sin(7t) because it has a named inverse (the arcsig) "despite..." I really am surprised that it has taken so long for anyone to point out this flaw. - the failure of the simple inverse to exist in many-to-one mappings like the sin / arcsign.
Congratualations.
The "rescue" of my proof gets a little complex and I did not want to do it, until forced. Basically every many-to-one mapping must be broken up into "indexed segments" For example, to stick with my original example of the A=sin(x) and working in degrees: Seg1 = 0<= x < 90 has the inverse (continuing my original notations of lower case letter with a prime/single quote for the inverse function) of a'1.
Seg2 = 90<= x < 270 with inverse: a'2
Seg3 = 270<= x < 450 with inverse a'3 etc (each segment spanning 180 degrees except the -90 to +90 segment is two.)
Now it gets very messy. I can no longer say:
t = a'(A,B,C...) = b'(A,B,C...) = c'(A,B,C...) ... and then reduce the number of equations by one by dropping the first (the t = ). Instead I must do something like:
tx = a'x(A,B,C...) = b'x(A,B,C...) = c'x(A,B,C...) and,
ty = a'y(A,B,C...) = b'y(A,B,C...) = c'y(A,B,C...) and,
tw = a'w(A,B,C...) = b'w(A,B,C...) = c'w(A,B,C...) and, ...etc.
where tx is that small interval of time common to all the one to one segments of the mappings on the right side of the first equation. etc. That is when any physical observable of concern begins to repeat, I give a new index number.
This seems very strange, but you are very familiar with this scheme. The Earth repeats it position after a year of travel around the sun. In contracts you sign, it is no good to have it stated that your mortage is completely paid on 30 June. You must give an index number for which 30 June. That is the current index number for the repeating position of the Earth going around the sun is 2005. That is all that is required, in principle, to rescue my proof, but it is very messy.
In physic, as normally used in the equations giving the functional relations between interacting objects, we neglect many things. For example, the gravity of Pluto is rarely consider even when planning a rocket trip from Earth to Mars. That is, the observables A,B,C,... are not, in pratice, of significant importance to consider many of them together. Thus, when eliminating time variable from a set of equations, it is only a relative short set, not the infinite large set of my formalism, that are used. Admitedly, if one is eliminating time from the equations which describe a physical observable which repeats in a short period, the "inverse function segments" will also be short. My example of the grandfather clock pendulum is a good illustration of this. Before the weights driving the clock mechanism need to be wound up again, the "index parameter" will achieve some rather large numerical values, but we always have an infinite supply new values, so that is just messy, not a problem. I might need to speak of half pendulum cycle 479,867,952 etc. for some segment of the inverse connecting the observable pendulum position to the variable "t" I am eliminate, piece-by-peice.
I will not go into such detail about your other concern where the sequents of events is either "random" and/or discrete (coin toss good example of both). Basically to rescue inverses, one simply makes a list and indexes it also. For example "head 475" "Tail476"... correspond to t475 and t476 respectively and one now has the required inverses, although they are not analytic functions - they are tabular functions. Given any t in the table one knows the H or T event. Given any H or T event in the tabulation one know the correcting t variable - I.e. not a problem to define the function or its inverse here either.
reilly said:
...tensors of Riemannian geometry. This is not easy stuff.
I agree. I was alway impressed by the compactness of tensor notation, summation being implied by repeated indexes, etc.
reilly said:
But, for the most part, we use physicist's time t for pure convenience -- some times physicists go so far as to use an imaginary number for time. Time exists? We're certainly programmed by evolution to have an innate sense of time. To the extent that we say tangible things exist, then our neural time-structure, probably exists, and clocks certainly exist. So, what are the criteria to judge whether time exists?
I agree the function of time approach is very convenient and very deep in man's thought patterns. As I think many lesser things are innate, I believe it is even innate. Glad you mentioned imaginiaryt - it does have some very useful applications. I should have mentioned it as many would be more inclined to understand that regular time variable t is also just a convenience.
Not really possible to prove nonexistance on anything; however, if one can demonstate, the postulated thing does not cause anything (and as an obvious consequence of this, is not observable) and that it is not necessary even for the discription of anything, then I for one am willing to assume the postulated thing does not have any claim to ontological status.
You definitely threw the best rock at me yet. Warm Regards, Billy T