I am New to Your Group as I Just Joined Yesterday.

cool, welcome.

Aspen Hello.

A Colorado handle? So is mine. Thanks for the welcome. I have read several of your post already. and Thanks for the comment, 

A quote turn out to be the best way to comment because it gets a white background and it is the easiest to read. I will utilize that whenever I can.

Bye

Thanks Elroch, that wasn't the proof.  I truly respect your opinion.  I hope you will give it after this proof.  This is easy but not short.  It is , but no one would understand the short version.  Simple , simple math.  We understand 10.  Some times written 10**1 , and we understand !0**-1 or one tenth.  We are going to define a very short time called a "dick", a small part of a second.  Lets try 10**2 or 100.  We are still OK with that.  And 10**3 or 1000, still OK.  How about 10**-9 or a nanosecond ?  OK ?  now 10**-10 or a tenth of a nanosecond.  It's getting a little harder.  We went from 10**-1 to 10**-10  and things started to get hard  .   How about 10**-100 .  You have no idea what that is. 

On the contrary, as a mathematician, I am happy with all numbers!

Do not feel bad , neither do I. For example there may only be 10**90 particles in the whole universe.  I did see Greene use the  number 10**500 as the total multi universes.  What does the number 10**1000 mean ?  Or 10**-1000 mean ?   I have no idea.

But I do!

That is only 3 zero in the  exponent.  Only 3.  Now the difference between discrete time and continuous starts.  If time is continuous than we can make it as small as we want.  How about 10**-1000000 part of a second ?There is not a single person on earth that will understand that number.  Or how about if the number of zeros goes around the room you are in and then back to the second line under 10**-10000................00  That's not a dick.  How about around the earth.  No around the universe. No the zeros go around the universe once for every one in the first time around,  That's a dick.  This is a very small unit of time.  AND there are an awful lot in a second.  And what must nature do in that much time and how often will nature need to do that ?     Part 3 next. 

I agree that there are units of time so small they are not physically useful. Basically anything a lot smaller than the Planck time falls into the category.

Part 3.   What does nature need to do in a dick ?   Well in order to figure how two particles will move relative to each other, nature will have to figure out how every other pair of particles also move.  It can not make one mistake , or all our "laws" go haywire.  Then it needs to do the same for the next pair, etc,etc.  You can tell how many pairs that is if  you assume there are about 10**90 particles.  Oh;  and then you must do it again and again and again, just to get to one second.  Now, that should be good enough for any one to understand that nature can not do that, but I am sure some one is saying , yes it can.  Remember, we started with time is continuous.

This is a classical (i.e. non-quantum gravity) assumption. Time is not continuous at the smallest level, because space-time turns into a sort of froth (with more dimensions to make things even worse). It is an excellent approximate to say it is continuous at much larger times. A good analogy for this would be measuring distances on a piece of cloth. If you try to measure distances at the scale of the diameter of the fibres, you have problems. Assumptions about the two-dimensional nature of the material fall down, also assumptions about its symmetries. 

 So a small dick is; take all the zeros in the exponent and also use them in the base, (replace the 10)  .   1000**3 = 10**3 * 10**3 * 10**3 , or 10**9  0r the exponent squared.  Do you still say; so what ?     Well, I saw this trick too.  Again used in inflation. There they double all space 2**100 times and have no problem telling us that is easy.  So lets just double all the zeros, again and again, say 100 times.  I am only doubling zeros , they doubled space, zeros ought to be easier.  Now you might figure nature does not need time to figure out how two particles will move.  Nature doesn't need time.  Well then nature would have known the end of the universe before the Big Bang started, so why do the Big Bang  at all ?   Some still won't believe this.  Time is continuous, PERIOD.  I might add here that nature will have to do that not only in our universe, but for all 10**500 universes in the same very small dick.   And that's hoping that no two universes interact.  For those of you that will give it a try,   Next part 4 will be the  conclusions from considering DISCRETE TIME. 

If nature can not see into the future, then a particle only knows NOW.

This is a really interesting point. In all physics, the progress of time is predictable through differential equations. So a sort of snapshot of now in quantum mechanics is enough (technically it provides boundary conditions for a differential equation). In general relativity (and relativistic quantum mechanics) its a little more complex, as there is no global now, but the idea of specifying boundary conditions (in 1 lower dimension) works fine. These ideas all generalise to the speculative theories such as string theory.

It's worth emphasising that the differential equations of QM and GR are just a large scale approximation to things that at the Planck scale are frothy and space-time breaks down.

There are no fields.  No quantum mechanics.  An electron in orbit does not know there is a proton around.  A particle only knows now.  We know the solutions to QM fit the data. The math is right or close, but the concept is wrong.  In the two slit electron experiment, the electron NEVER sees two open slits ahead of it.  Never.  What is happening.  If you do 10000 experiments and use only the first electron you will get one result, If you use  the 1000th electron you will get a second result and if you use the 10000 electron a third result.  Try it and win the Nobel.   The electrons as they pass thru one slit will "bump"  into the walls of the slit. Thus their initial conditions on the rest of the path to the detector will be the same except for slight directional differences.  There is a major difference between the first electron and the last electrons in this experiment.  The last ones all cross a path in space that only the electron from the other slit went through.  The first electrons never see this space as no other electrons have passed there yet.  That space, a spock, for space block, contains energy that is given  to the second electron that will move it  off of its course.  The space is called an "energy chain" and is responsible for other events that we see in nature.  Namely action at a distance, faster than light neutrino, stronger gravity. Stibility of atoms and protons.    (well if you are still interested , please send me a note.  You are welcome to read the 33000 word ruff draft of "Time and its Properties") 

The two slit experiment gives statistics that show that individual electrons exhibit self-interference, resulting from a wave passing through both slits. If you have a theory that involves electrons going through one slit, you will fail to predict the right statistics, disproving your theory.