Tom's theory

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by EBTX</i>
<br />Wouldn't it be better to say that in any N dimensional manifold N-1 dimensions are relative?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">I took the original question to be one of physics, not mathematics. In physics, all known descriptions of nature can be reduced to five dimensions.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">We have to hold one as a "standard of measure" to say anything objective about the others.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">That makes no sense to me. The three space dimensions can all be expressed in space units, but time and scale cannot, nor can they be related to each other. What are these mathematical dimensions that can be related? -|Tom|-

Just take the three space dimensions. If length, width and height are all relative no objective measurement is possible. You would have to define one as absolute and use that one to measure the others.

If everything is relative, you have "nothing to stand" on so to speak.

EBTX,

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by EBTX</i>
<br />Just take the three space dimensions. If length, width and height are all relative no objective measurement is possible. You would have to define one as absolute and use that one to measure the others.

If everything is relative, you have "nothing to stand" on so to speak.
<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Isn't measurement always relative? I mean, we could use my laptop's width as a unit of length to measure objects at any scale (I know, not a particularly reliable measure). The unit of length is really arbitrary isn't it?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by EBTX</i>
<br />If everything is relative, you have "nothing to stand" on so to speak.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">That is a necessary feature of infinite dimensions. Only finite intervals, which are always relative, can be measured. -|Tom|-

Is there a relationship between scale and time? Does time slow down, for example, at larger scales?

Also, Tom, your suggestion that our sun might be a proton in a larger scale (or that protons in our scale might be suns in smaller scales) is just a metaphor, right? Unless I'm not understanding something, the difference in size between our sun and a proton doesn't seem large enough for this to be the case. It is more likley that our sun, in larger scales, correlates with particles much smaller than a proton.

Or am I not understanding sub-atomic distances and their relationship with astronomical distances?

Emanuel

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by emanuel</i>
<br />Is there a relationship between scale and time? Does time slow down, for example, at larger scales?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Yes and yes. Actually, time and scale are independent dimensions. But in MM, time is not some physical thing. It is just a measure of change. And on larger scales, change occurs more slowly than on smaller scales. So time seems to pass more slowly.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Also, Tom, your suggestion that our sun might be a proton in a larger scale (or that protons in our scale might be suns in smaller scales) is just a metaphor, right? Unless I'm not understanding something, the difference in size between our sun and a proton doesn't seem large enough for this to be the case. It is more likley that our sun, in larger scales, correlates with particles much smaller than a proton.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Yes, you are right again. I was trying to say that the same kinds of forms might occur at any scale; or better, that our scale is in no way special (except, of course, that it is <i>ours</i>). -|Tom|-