Re: dimensionality of mass part one

Posted by rtharbaugh on May 12, 2003 at 11:35:21:

In Reply to: Re: dimensionality of mass part one posted by DickT on May 11, 2003 at 08:49:19:

Dick

Yes, this is interesting, and points to a conceptual problem for which MTI provides a possible solution.

The problem is that if a proposed partical is pointlike in time, it cannot be said to exist in any meaningful way in space. However if a proposed partical is pointlike in space, it can still be said to continue along a line in time. This is the notion we have called location. A location, you see, has a position in 3-space, which implies continuity in time, but it has no bulk, which is to say, no measurable dimension in xyz.

Location is everything, isn't it? How would we do physics at all if there were no continuity of location in space and time?

SO this seems to show that space and time, as is the common perception, are not at all the same thing. We can say that a proposed partical has no dimensional representation in space, but we cannot meaningfully say that a proposed partical has no dimensional representation in time.

Yet we know from our beautiful mathematics that space and time equate through velocity. How can space and time be the same and yet not be the same?

The answer in MTI is that the seeming problem is one of perspective. Each of us has a conceptual model (a kind of gedanken laboratory) upon which is displayed the information we recieve via the senses from the universe. As humans, we seem to have an ability to extend our model to three dimensions in space and one in time fairly easily.

Most humans do this routinely, and you don't have to know any physics at all. Consider the complexity and subtlety required to play basketball. A good player has to have an idea of where the ball is in three dimensions, plus an idea of where it is going to be in the three dimensions as modified into the future. This is not all. A player has to correctly judge not only distance and velocity, but also has to deal with accelleration as he or she applies force to the ball to make it move in the required trajectories.

So we can see from this that nature has provided us with a platform upon which to construct a model of the universe that easily goes beyond three dimensions in space and one in time. Accelleration involves three dimensions in space and two in time. And there is an important question about the space dimensions. Are the ones you see now the same as the ones you see five minutes from now?

Of course they are not the same, but are translated through time. If they were the same, the basketball court would fill up solid with basketballs in very short order. Clearly the space dimensions must be completely different, altho they still look the same in some respects, from one instant to the next.

The lines on the court, for instance, exhibit a high degree of continuity in time and space. They don't move around much. If they did, the game would be much more difficult. In fact, we define the lines on the court specifically not to move around much, so that we can base the rules of the game upon their constancy.

Again, the notion of location. Some kinds of things mostly stay put. We can pick a thing, like the earth or the sun, and say it stays the same in space through time, and define the location of everything else in the universe accordingly. The floor of the basketball court moves around very little compared to the motion of the earth, so everything works out all right for the player. He doesn't have to worry that the net will not be in the "same place" when he comes back to it.

Of course we all know that the net is not in the same place at all. Due to the various sidereal motions it is in fact miles and miles from where it was last time he threw a ball at it. But it doesn't matter, much, because everything on the court has translated through space together. The player can neglect the motion of the court relitive to Venus and still make a basket.

Let's look at that again. The player knows the basket will be in the same place. The physicist knows it is not in the same place. Good thing the player isn't thinking of sidereal physics. The problem of getting the ball through the net would be much more difficult. In the gedanken laboratory of the player, the court does not change, at least not for the duration necessary to play the game. The player is justified in considering the location of the court to remain "the same."

We see our world as remaining mostly the same in the same way the player does. We build a house on a lot in the city and expect it to still be in the same place when we get home from work. There is no apparent contradiction in the fact that it is really thousands and thousands of miles from where it was eight hours ago. We are quite safe in considering the location the same, even for years and years and years.

I hope from this discussion that it is now clear that the spatial dimensions x,y, and z are not the same from instant to instant at all. It is merely a matter of convenience that we consider them to be the same, when in fact they are constantly changing.

Then here is the leap.

If space and time are the same, it is not because time stands still in the same way that space seems to do. It is because space shifts around with the same degree of fluidity that time does. There is no location. There is no pointlike partical. Location may seem to be everything, but we know now that it is nothing at all but a fictional convenience, albeit one which we find extremely useful when shooting baskets and doing physics.

Pianowow says that I have abandoned the solid reliable world of science and entered the indistinct world of metaphysics. What is mass? Not a question for science, but in the same catagory as "Why is mass?" Science is not interested in what or why mass is, but only in what mass does. Mass is accepted as existing without need for further explanation. And this is certainly good enough for basketball.

But we as humans are now developing tools which reach way beyond the basketball court, and we must find ways to fit the information they give us into our conceptual model, our gedanken laboratory. Well. At least we on this board find it interesting to do so. I suppose Micheal Jordan can enjoy his millions perfectly comfortably without ever wondering about superstrings.

Our platform does not have to support a gedanken laboratory in more that 3+1 dimensions to get us home at night. Why should we constuct an intellectual model that requires us to imagine more dimensions than the four we usually know and love?

I did not invent the question, I am merely trying to find a reasonable way to approach an answer to it. The question of extra dimensions, and of the nature of mass (why does it do that?) was presented to me through the graces of quantum and superstring physics. There are still those who scratch their heads and wonder how quantum physics can be called a science. Maybe it is more like astrology than science. Yet it seems to work to a remarkable degree. Quantum, I mean, not to degrade astrology, but quantum has more decimal places.

Actually I think there are a lot of scientists out there who are not happy about welcoming superstring theory into the club. Make a prediction, they say, and stick to it. We can't do that yet. Well. I stick my neck out and predict we won't find gravitons, but that is not the same as saying we won't find evidence of gravitons. Evidence of bigfoot and ufo's is common enough.

So I am suggesting that we all need to add on to our gedanken laboratories if we are to make sense of things like black holes and antimatter clouds. In fact, we need a basic structural remodeling. 3+1 just doesn't do it anymore. We need to accomodate five and seven and nine and ten and eleven and nineteen and twentyone and twentysix and what else? Name that dimension.

I suggest we start by recognising that 3+1 is a filter through which we look at things around us. The things themselves exist in a kind of dimensionality of their own. Maybe some of them are one dimensional like the hypothetical x partical (string). Maybe some are two dimensional like branes, maybe some are three dimensional like basketballs. Then if there are things, there must be a not-thing background from which the things may be said to be independent. What is the dimensionality of the not-thing?

Any observation then, even on the basketball court, is qualified by these three conditions. The observer has a model (1) upon which is displayed sensiate information about the condition of the object (2) as compared to the background (3). The model, to be useful to the observer, must select or conform to the information about how the object is different from the background. We select certain features for display and ignore others.

As observers, we have (potentially) unlimited control of the model, some limited control of the oject, and no control whatsoever of the background. We have discovered, partly through the use of mathematics and partly through the use of observation, that some objects cannot be displayed fully on a 3+1 model. This is disconcerting because we are very proud of our ability to view 3+1, which we have only been able to do for the last hundred years or so. But clearly it is not good enough to stop here. We have to go on to higher dimensional models.

The idea that the "extra dimenesions" are curled up somehow too small to observe from our 3+1 model is therefore inadequate. We can deny that extra dimensions exist and get along quite well, or we can remodel the laboratory. I think we will make more progress by the latter attempt, even if it is dusty and confusing for a while.

First, I suggest instead of ssst, (the 3+1 model) we go right on to the ssstt model. This should not be much of a stretch since we are quite familiar for the past three centuries with accellerated spaces. Then we can stretch a little and go to sssttt, which is evident in our classical view as the physical quality called jerk. Now in momentum we have the term C^4, which gives us sssstttt. It should be no suprise that these quantities are not easily displayed on the 3+1 model. It just plain isn't big enough to hold all the data.

Then, we already are used to x,y,z in place of s,s,s, and it seems we may need to add w to the spatial list. All those t's are different too, so for now let us think of them as a,b,c,d. So in dealing with momentum we need to consider a model like w,x,y,z,a,b,c,d.

I'm sorry, I can't do it. I am still enshrouded in my good old 3+1. Fortunately, there is a way to cheat, and we do it all the time. It is called perspective. We can use a set of rules (perspective) to project a 3d image onto a 2d surface. We look at a picture of our family and recognise immediately that dad is standing behind mom. We are not concerned, much less terrified, that dad's torso seems to be missing.

In the same way, we should be able to project this eight dimensional momentum system onto a 3+1 dimensional model, probably by using more than one view at first, to get all the details in. We have to look at several 3+1 views to see all of the 8d object, just as we would need more photos to prove that dad was not missing vital parts. Eventually we may be able to see the photo of mom and dad and not get upset, just as we may be able to look at our 3+1 idea of a black hole and not get squeamish about the time-space contraction "problem". With the proper conceptual model, there is no problem. Dad doesn't need to go to the hospital and the black hole doesn't need to be fixed either. We just have to look at it different.

I have to take a break but hope to return to the remaodling project later. Thanks for being here.

RTH

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