Is there a googolplex of anything in this universe? (1 Viewer)

[RogerB]

:frowning:

 

[RobertR]

In fifty years we might discover smaller particles than quarks

Ok, but the corollary to my previous question is, is there a limit to to how much smaller particles "might be"? And if so, that would place a limit on how short a time interval there could be. I suspect it's longer than 1/googolplex of a second.

 

[StephenK]

Is time infinitely divisible?

The answer is actually no.

Time, like everything else (except gravity which has not been "quantized" yet), can be broken down into a "smallest particle that cannot be sub-divided" or quanta.

This has been theorized as 10-43 (that's 10 to the neg 43) sec, also called Planck Time. Under this threshold, the very meaning of time ceases to have meaning. Don't ask me why, I'm not a physicist. The weird thing is, things happen all the time in less than this theoretical limit. Certain particle decay requires the breaking of the law of energy conservation. But, theory goes, if this happens in less than Planck's time, then it hasn't actually happened and thus no law is broken. Basically, the particle "borrows" this energy from the ether to do its thing then gives it back before the time is over and its all ok.

Gotta love that Quantum theory...

 

[BrianW]

It seems likely that the Planck Length would impose a lower limit on the size of a given particle. But don't let that fool you into thinking that the lower limits have been probed, or even imagined. the Planck Length is about 100 billion billion times smaller than a proton.

I believe that efforts to quantify time have been fruitful, except where gravity is involved. When it comes to the curvature of space-time, all efforts to apply a method of quantization have failed miserably, and we continue to think of gravity and the space-time continuum as continuous in nature. But that doesn't necessarily make it so.

Still, the Planck Length, if taken to define the smallest unit of distance, can be used to derive the smallest unit of time (the amount of time it takes for an object to traverse the Planck Length), and Robert's right: There ain't a googolplex number of divisions in a second.

 

[StephenK]

Brian, beat ya to it!
great minds think alike....

 

[Kevin P]

This has been theorized as 10-43 (that's 10 to the neg 43) sec,

That doesn't even come close to a "googolth" of a second, much less a "googolplexth" of a second! A googolth of a second is 10^-100, and a googolplexth is 10^-(10^100).

I bet there isn't even a googol number of anything in the universe (isn't there only about 10^50 subatomic particles in the entire universe?). In order for there to be a googol number of as yet undiscovered sub-sub-...-atomic particles, you would need an average of 10^50 of them in every subatomic particle in order to wind up with a googol number of them in the universe. It's not likely.

A googol written out is 10,000,000,000,000,000,000,000,000,000,000,000,000 ,000,000,000,000,000,000,000,000,000,000,000,000,0 00,000,000,000,000,000,000,000,000. The number of particles in the entire universe is about half as many digits (if my 10^50 figure is anywhere near close!)

It's impossible to write out a googolplex, it would be 1 followed by a googol zeros.

KJP

 

[StephenK]

Anyone remember Cosmos with Carl Sagan?

I remember one episode where he talks about this and I remember him saying that a piece of paper with a googleplex written on it could not be "stuffed" into the known universe. Pretty cool.

Damn, I wish that DVD boxed set wasn't so expensive!

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"Character is what you are in the dark" - Lord John Whorfin

 

[Randy Tennison]

Ok, here is something that has always given me a headache.

If time is infinately divisible, then distance must also be.

If any distance is divisible, then we should never get where we are going. If you are going to walk a mile, first you have to walk 1/2 mile. Then you would need to walk 1/2 of the next 1/2 mile, or 1/4 mile. Then, 1/2 of that 1/4 mile, or 1/8 mile, etc. etc. etc.

You should never be able to reach your destination, as you always have at least 1/2 of the remainng distance to travel.

Ouch. Brain cramp!

 

[RobertR]

If any distance is divisible, then we should never get where we are going. If you are going to walk a mile, first you have to walk 1/2 mile. Then you would need to walk 1/2 of the next 1/2 mile, or 1/4 mile. Then, 1/2 of that 1/4 mile, or 1/8 mile, etc. etc. etc.

But it also takes only half the time to traverse each succeeding fraction. And we know that the infinite series 1/2 + 1/4 + 1/8....converges to 1.
So you do reach your destination after all.

 

[David Lawson]

n. The number of spins any given song will receive on a radio station owned by Clear Channel.

 

[BrianW]

Kevin: Nice post. I've met way too many people who think that since we have 10^50 particles in the universe, then we're half way to reaching a googol.
Stephen: D'oh! I've been googolplexthed!

 

[Randy Tennison]

Robert - If it's infinite, how can you ever reach the end. By the defination of the word, it is not finite, and therefore, can never stop.

Oops, there I go, I've gone crosseyed again.

 

[RobertR]

If it's infinite, how can you ever reach the end.

For the same reason that an infinite number of rectangles fitted to a curve (as in calculus) adds up to a finite area.

An infinite number of things can add up to a finite quantity.

 

[Kevin P]

Kevin: Nice post. I've met way too many people who think that since we have 10^50 particles in the universe, then we're half way to reaching a googol.

Half a googol is 5 * 10^99, or 5 followed by 99 zeros. Quite a bit more than 10^50 (1 followed by 50 zeros). Those zeros count for a lot!
Dang, I sound like a geek! Must be because I are one!
KJP