Simple Math and quantum phyiscs 5 x 0 and e =mc2?

[spacecowboy27]

Ok this is probably going to sound like the gibberish of a crazy fool but its been awhile since I have done any deep thinking so I am a little rusty. I recently began wondering if one of the reasons why quantum physics and the standard model of particles have so many weird constants and unanswered questions simply because of the way we are using our mathematical system which include non-existant numbers to try and explain it.

The problem came up when I tried to explain any number multiplied by 0.

Its easy to explain in simple terms why 2 x 5 = 10 because you can say that if I have 5 groups of 2 apples and add them together the total sum I get equals 10. And its easy to show.

2 + 2 + 2 + 2 + 2 = 10

Likewise math allows me to re-arrange that and say that if I have 2 groups of 5 apples and add them together I get 10 or 5 x 2 = 10.

5 + 5 = 10

The problem arises when 0 comes into play, 0 x 5 = 0, according to math. Its easy to say that if I have 0 apples and add them together 5 times I have 0 apples.

0 + 0 + 0 + 0 + 0 = 0

But that should be re-arrangable, and I should be able to explain 5 x 0 in the same manner. In reality, however that is not possible or makes no logical sense. In other words I cannot say that if I have a group of 5 apples and add them together 0 times, whatever that means based on your definition of 0, I get 0. That to me makes no sense.

In real life, I suppose it could be explained as I never peformed my operation.

Because I certainly have 5 apples so I suppose 5 x 0 = 0 must mean I never performed my operation, right? Else 5 x 0 can only be explained one way. And that is the first way, with the value of 0 being the one added to itself a total number of 5 times.

But what if I did in fact perform the operation like that and try to explain it and still make sense in reality? Well using the same explanations as above it would mean that I could take a group of 5 apples and add them by 5 a certain number of times and somehow I end up with no apples at all. That number according to the equation is 0. But it has no real value, in a way it does not exist. Or does it?

What if we go further and apply it to quantum physics.

Could that number of times be "infinity"?

Would it explain why a black hole even exists? Because with quantum physics and correct me if I am wrong I can logically say that the more times I add a particular mass together, the closer I get to the reality that it would be so massiveand dense it would create a black hole and thus in my reality it would indeed destroy itself and the apples would be gone...which would make my math correct and equal 0.

So is 0 and infinity one and the same? Well they seem to have the same properties in that certainly neither is actually attainable, possible or exists in the "tangible" world. Or is 0 a gate? To a parellel universe? Is 0 the black hole itself? Do we need to cast out 0 all together out of math and devise a new system altogether?

In quantum physics, E = mc², and the conservation of mass/energry states I cannot destroy matter completely without taking account energy, something rudimentary math does not account for. Unless, I take into account the possibility of a black hole. And if you take that into account well what I did when I performed 5 x 0 is I have created a black hole, massive energy, and destroyed the apples in my universe.

And it should mean that I no longer have any apples but instead I have released energy in the amount of the apples mass traveling at the speed of light squared by Einstein's equation.


So perhaps 0 in the case of 5 x 0 does have a value. Perhaps 0 and infinity have the same value, in that it is actually the number of 5 unit masses I would need to put together in order for that mass to destroy itself.

Thus for different size masses 0 and infinity would actually have a real numeric value, and it may even be a constant.

I don't know how to perform the calcuation but I would be interested in finding out if somehow all of this related back to the speed of light. In other words if the number of times I would need to add or condense this particular mass together for it to destroy itself, is equal to the speed of light or a factor times the speed of light.

Then perhaps light, existence, 0, infinity and "life" are one and the same.

If anyone has actually followed my argument all the way, then I guess my question would be does anyone have a better explanation of why 5 x 0 = 0 and 0 x 5 = 0 using the same rules that you use to describe why 5 x 2 = 10 and 2 x 5 = 10?

Note that I am not asking for a derivative mathematical solution, but actual english terms. Unless your derivative solution can in of itself be explained using english terms that make logical sense in reality.

 

[Feldoh]

Huh?

0 x 5 You have zero groups of 5 apples (Nothing, as you said)

5 x 0 you have five groups of 0 apples (0+0+0+0+0)

Your 'if' makes no sense you cannot add any amount of 5's to get zero other than 0.

All you said was assume 0 = infinity. In which case you've defined infinity in such a way that is different from the infinity we typically use. It's just a word that we assign meaning to, all you did was assign it to a different meaning that is not traditionally used.

We could easily call 5+5+5+5+5+... (adding 5 forever) some other word: blue. Blue is now the mass of a black hole. Mathematically, all I have done is change the value with which the word is associated.

 

[Hurkyl]

You've gone off onto lala-land -- you need to ratchet the speculation way down.


The integers are a number system. They have a precise definition. The arithmetic you learned in elementary school conforms to that definition.

People use the integers to "count". We've found that labeling collections of real-world objects by integers is useful for understanding. We've found that certain things we do with collections correspond to the integer arithmetic operations. This is very useful, so we use it.

Integers, and their arithmetic, are similarly applicable to a wide variety of subjects. That's why we learn them in elementary school.

Integer arithmetic doesn't apply to some things. If we add one puddle of water to one puddle of water, we get one (bigger) puddle of water. This doesn't tell us anything about integer arithmetic. This just tells us that we shouldn't use integer arithmetic in this way when playing with puddles of water.

If you don't want to deal with empty collections, that's your choice. But that choice doesn't tell you anything about the arithmetic of integers. It's also a shame, because understanding "degenerate" cases is usually very enlightening.

 

[spacecowboy27]

Huh?

0 x 5 You have zero groups of 5 apples (0+0+0+0+0)

5 x 0 you have five groups of 0 apples (Nothing, as you said)

Your 'if' makes no sense you cannot add any amount of 5's to get zero other than 0.

All you said was assume 0 = infinity. In which case you've defined infinity in such a way that is different from the infinity we typically use. It's just a word that we assign meaning to, all you did was assign it to a different meaning that is not traditionally used.

We could easily call 5+5+5+5+5+... (adding 5 forever) some other word: blue. Blue is now the mass of a black hole. Mathematically, all I have done is change the value with which the word is associated.

No. I DO in fact have 5 apples. That is my starting point. And that is precisely my point. If I start with 0 then you are correct, I could have 5, 6 or a million groups of 0 apples. It is still 0.

But I DO have 5 apples. I am adding my apples by a factor. That factor is my second number and when that factor is 0 it no longer makes any logical sense any more than 1/ 0 does. Math tells me if I multiply it BY 0 I get 0.

See for 5 x 0 the way you just described it, you are taking my apples completely out of existence in order for you to reverse the equation and explain it in the manner you just explained.

It makes sense to say I multiply 0 by a factor and still get 0.
But actually stating it the reverse way, makes absolutely no sense unless you tell me I didn't have any apples to begin with.

"The integers are a number system. They have a precise definition. The arithmetic you learned in elementary school conforms to that definition."

And that was precisely my point. What if that's not entirely accurate or should I say sufficient enough to begin with in being able to explain everything that is currently going on with quantum physics.

The system was designed for us to be able to understand things in a way that is easy for us to understand and work with. But that doesn't mean that we are going to force the universe to unveil itself and its mistery in this particular language that we created.

 

[Feldoh]

You never had any apples regardless of how you state it.

You have 5 apples in zero groups as far as your analogy goes. Say you have five apples and 0 tables, you still have 5 apples but you didn't put them on any tables so the total number of apples on the tables in 0.

You essentially excluded the apples from your groupings.

 

[Hurkyl]

You have 5 apples in zero groups

You can't have five apples in zero groups.

You essentially excluded the apples from your groupings.

You can have five apples that aren't grouped

 

[Hurkyl]

And that was precisely my point. What if that's not entirely accurate or should I say sufficient enough to begin with in being able to explain everything that is currently going on with quantum physics.

If we can't use the integers to understand some aspect reality, then we'll build some other construct to understand that aspect of reality.

Quantum mechanics, by the way, talks about mathematical structures just like the integers. And like the integers relate to counting, science has shown us that quantum mechanics is useful for describing microscopic reality.

(Unlike the integers, quantum mechanics is a field of study, so there are various different structures that one might consider, and so forth)

 

[spacecowboy27]

You never had any apples regardless of how you state it.

You have 5 apples in zero groups as far as your analogy goes. Say you have five apples and 0 tables, you still have 5 apples but you didn't put them on any tables so the total number of apples on the tables in 0.

You essentially excluded the apples from your groupings.

Well you don;t actually have to use groups.

But using that you just came to the same conclusion that I did in my thread.

That I never performed the operation.


So 5 x 0 = 0 means I never went through with my operation. So surely you see why it is a more accurate way of describing instead of just saying 0.

So at least you arrived half way to the same point I did.

Now go beyond that and actually tie it into quantum physics.


Oh and also regarding you stating that I re-defined infinity to another word. No I assumed it was 0. In other words if what you say, is that infinity = blue, well then blue = 0.

And you would not be wrong to state:

5 x infinity = infinity. That actually makes sense.
5 x 0 = 0 makes no logical sense, if the operation did indeed take place in that sequential order, unless 0 is in fact one and the same as infinity.

Just like you can never truly reach infinity in the real world...I also don't believe that there is such a thing as 0, in the real world. If it is - then it cannot exist. Its a paradox in of itself. But if it did, it could be the same as infinity. In other words the more you add to something(moving towards infinity), then the greater the chances that you will end up with 0 or that objects destruction or non-existance. Of course that would only be true if indeed a black whole would get created simply by adding to the mass of an object.

Which is why I would really like to know how to obtain the point at which an objects own mass and gravity begins to implode in of itself? Is that even possible.

 

[Feldoh]

Hmm so I understand it like this:

Having some quantity of nothing means that you still have something even though you have nothing of the something?

 

[spacecowboy27]

If we can't use the integers to understand some aspect reality, then we'll build some other construct to understand that aspect of reality.

Quantum mechanics, by the way, talks about mathematical structures just like the integers. And like the integers relate to counting, science has shown us that quantum mechanics is useful for describing microscopic reality.

(Unlike the integers, quantum mechanics is a field of study, so there are various different structures that one might consider, and so forth)

I agree. And I would be interested to know if anyone has ever tried to look at quantum physics and perform calculations with a mathematical system that does not inlcude negative numbers, 0 and infinity. Perhaps one not even based on the metric(and certainly not english) system.

 

[spacecowboy27]

Hmm so I understand it like this:

Having some quantity of nothing means that you still have something even though you have nothing of the something?

No, having a quantity of nothing means you have a multiple number of 0s. And that does not equal something. It equals 0. I agreed with that part. I never contested that.

You are twisting my logic.

Its trying to explain it the opposite way, when you start with 5, in that sequential order...that you cannot do it without reversing the equation and stating that I had no apples all along. But the truth is I did. I mean after all if I have 5 apples in my basket, I DO have 5 apples in my basket.

5 x 0 = 0 doesn't and should NOT mean I have no apples. In real life it should either mean I did not perform my operation, or that this 0 made my apples vanish. Or TURNED my apples into nothing, their non-existance. However Einstein said that I cannot destroy matter completely. Right? So that can't possibly be true without also adding the other side of the equation which is E.

In real life.

See I begin the equation by stating that I DO have 5 apples. This is a fact. I am telling you this. You cannot complete your operation and come back and tell me that I didn't have any apples all along. You broke the control factor once you do that.

For that to be true, and for your 0 to work, you have to change the reality that I have 5 apples.

 

[spacecowboy27]

Another way of looking at it, is with variables.

Math says I can do this.

B x A = C or C = AB or A x B =AB

Which according to math I can also write this as:

A = C/B or B = C/A

Now this is true for every real number and negative number.

If A = 2, B = 3 then what we have is

2 x 3 = C = 6

or 2 = C/3 or 3 = C/2.

The only problem arises when you introduce the number 0. Now all of a sudden math tells us one of those true statements breaks down and cannot be performed simply because of the sequence in which we are to approach it.

In other words if A = 0 instead of 2 we have

0 x 3 = C = 0

or 0 = 0/3 but we can no longer do the other expression which was true for all other numbers. 3 = C/0 is no longer mathematically correct. It is undefined.

 

[Hurkyl]

I agree. And I would be interested to know if anyone has ever tried to look at quantum physics and perform calculations with a mathematical system that does not inlcude negative numbers, 0 and infinity.

It's a very straightforward exercise to do so. You can get rid of the complex numbers, and even the irrational numbers.

The result will make exactly the same predictions, but it would be extraordinarily cumbersome to do even the simplest calculations or to formulate even the most basic concepts.

 

[spacecowboy27]

It's a very straightforward exercise to do so. You can get rid of the complex numbers, and even the irrational numbers.

The result will make exactly the same predictions, but it would be extraordinarily cumbersome to do even the simplest calculations or to formulate even the most basic concepts.

Well I would hope that is what would happen, or at the very least, that the system itself would not break down. My point is, by doing that can we observe some type of new patterns, or can we get different values for some of these constants that may lead to reaching solutions to some of the problems in modern physics like the gravity problem.

I started searching for other articles where this pesky 0 may cause other problems and came across this one written by Fotini Markopoulu from the Perimeter Institute of Theoreticaly Physics in Dec of 08.

One particular part that caught my interest was this:

The incompatibility of general relativity and
quantum theory can be stated in many ways and a classic one is the problem of time: adapting the Scrodinger equation to a dieomorphism invariant context by quantizing equation (1) gives the Wheeler-deWitt equation,

( I cannot copy and paste the characters of this equation but you can follow the link)

(2) (character x) is the wavefunction of the universe, (character y) is the quantum Hamiltonian constraint and 0 means there is no time. The problem with this shortest of equations is that we still do not really know what it means. After half a century of hard work, we have candidates for (character x) and (character y) but 0 is still causing trouble.

http://www.fqxi.org/data/essay-contest-files/Markopoulou_SpaceDNE.pdf

Paradoxes are usually resolved when we realize that a certain unstated assumption is lurking in the background which, under closer inspection, we see is false."

Now under my explanation the equation 5 x 0 = 0 does indeed create a mathematical paradox.

And just like the author of this paper, I am not trying to convince anyone of anything either. But rather spark a discussion.

And I am simply curious if our assumptions and definitions of 0, could be one of the problems. Perhaps one of those false assumptions is that 0 x 5 = 0 and 5 x 0 = 0 is the same thing. Ignoring sequence. As math tells us. Even though math itself breaks down in one of the examples I posted above.

Its funny that I came across that article because what got me thinking about this was the absence of the inclusion of gravity in the standard model of subatomic particles...just saying.