Antigravity Research

<b>[Jim] "He (Einstein) worked in approximations.</b>

That's close, but not quite right. The EFEs (field equations) and their various solutions discovered to date are exact.

IF ... you stay in the 4D universe of space-time.

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But we don't live there. We live in a 3D plus 1D universe of space plus time. (Actually, its 3/1/1 space/time/size (or mass). But that is a different story ...)

So, in order for us to verify Einstein's theories, all those exact equations have to be translated from (4D) to (3D + 1D). And that is where the approximations happen.

<ul>
We work with exact equations over there in the 'model' universe - but we verify against observation back here in the 'real' universe, using approximations .

For the most part this works very well. And yet, it leaves many of us with nagging doubts.

Subtle errors in logic ...

Basic questions we have stopped asking ourselves ...

Decisions made in the distant past (about what is or is not possible/reasonable/logical, about which of several theories best describes/explains things), without benefit of observations made and knowledge learned since then, are seldom re-visited to see if the new observations or new knowledge justifies changing our mind.

Hmmm.</ul>

These approximations are usually generated using the good ole series expansion techniques we all learned way back in first and second year calculus. Or even earlier in HS with AP math classes. Such approximations can be made as exact as we desire.

Suppose a new measuring tool is invented that adds two decimal places to the precision of a measured quantity, and suppose that this exceeds the precision of the current prediction. We just add a few more terms to the series we use to generate our 3D + 1D approximation of the 4D exact equations and our prediction precision is increased to the desired level. (Computers really help here.)

Predicted values (from either exact equations - when available - or from equation approximations) are never the same as measured values of course. This mismatch is caused mostly by our far-from-perfect ability to measure things. Measure something a million times and you get a million different (but mostly close) answers. That's why we invented 'error bars'.

And now we have a group of explorers that have found a measured value - including error bars - that is (absent that pesky 'hidden error source'), ever so slightly but still solidly different from the predicted value.

If no one can find a hidden error source, or figure out how to massage our understanding of the theory, it looks like the world of physics might be in for some changes. But these are some pretty big 'ifs'. Stay tuned for more developments.

LB

LB, I want to avoid the deep do-do here; what I meant is E=MC^2 is an approximation rather than absolute as assumed by most people. E=MC^2 has given rise to most of the silly ideas being currently being researched at huge costs not because it is right or wrong,but that it is an approximation.

Fair enough, Jim. No deep do-do here anyway - just a little history.

I am trying to shed some light on why we must use approximate equations instead of exact equations (for certain parts of the puzzle), when exact equations are in fact available (and in fact used for other parts of the puzzle).

I believe knowing <u>why</u> we do things helps us understand <u>what</u> we are doing. And that can help us figure out if we are doing things well, or not so well.

I guess another thing I'm trying to to say is - silly ideas do exist and approximations do exist, but there is no causal link between them. If the origin of silly ideas were that straight forward, they could be (and would already have been) banished.

Silly ideas come from somewhere else ...

Useful ideas are not silly and approximation is very useful-so is E=MC^2 useful. The silly stuff is all the invention done over several decades to maintain E=MC^2 as an absolute and the faith extended to true believers by decision makers that if we spend enough the truth will appear. The louder they yell the more they get.

<b>[Jim] "The louder they yell the more they get.</b>

Whether they deserve it or not. We certainly agree about this. It's one of the main points being made in the Big Science/Big Government forum.

But maybe I'm missing your point about "all the invention done over several decades". Perhaps an example or two would help me.

LB

It started with the neutrino which was invented to solve a problem and continues today with so many similar inventions. I was hoping the CERN work would end it, but they are looking for still other inventions.