Paradoxes and Dilemmas

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[Larry Burford]: c^2 is not a speed. Speed has units of distance over time, not distance^2 over time^2. And not (distance over time)^2.

[makis]: To be proper, c^2 is c^2. If you mean (c=2.99725E+8 m/s)^2 then that's not speed. But [(c=2.99725E+^2 m/s] is speed.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

That does not make physical sense. If I measure something as having a length l = 6 m, then l^2 cannot be [(l=6)*2 m]. That would be 36 meters if "l" is measured in meters, or it would be 0.036 meters if "l" is measured in kilometers, or 36,000 meters if "l" is measured in millimeters. In other words, if you separate the number from the units it is measured in, you get contradictions. It should be obvious after a bit of thought that the number in front of physical units is completely arbitrary, and could be anything whatever, depending on the choice of units.

The correct procedure is to square both the number and the units. Then the square of a length is an area, not a length. l^2 means that a square with length and width equal to l has area 36 square meters.

Likewise with c^2. The square of a speed is an energy per unit mass, and tells you how much energy would be dissipated by a unit mass converting all its speed into energy (as in an inelastic collision).

c is a number <b>and</b> a set of dimensions. They cannot be separated, or it would be impossible to write equations such as:
c = 299,792,458 m/s = 186,282 miles/s = 0.984 feet/nanosecond, because those numbers are obviously not equal. So it is not physically possible to interpret c^2 as a speed. It has the wrong dimensions. If you don't square the dimensions too, you get a meaningless number that could be anything.

IMO, this is not appropriate discussion material for this web site. If you are thoroughly familiar with these concepts and wish to raise a serious challenge to them with careful reasoning and citations, that could be appropriate if other experts consulted have no answers to your challenge. But IMO this is not the place to question elementary physics for no better reason than someone has never studied the subject and something goes against one's intuition. One should consult a physics teacher who gets paid to teach such matters, or a friend or relative who knows the subject matter already, or the appropriate USENET newsgroup to find strangers willing to volunteer.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[makis]: I would say the speed of light in general is C^n, n being the extra dimensions above 4.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

What "extra dimensions"? There are five and only five physical dimensions currently recognized, and they are presently sufficient to explain everything we observe in the universe. This is detailed in <i>Dark Matter, Missing Planets and New Comets</i>. Dimensions beyond these five are often invoked in pure math and in science fiction, but should not be confused with real physics. Again, you might wish to raise a serious challenge to that limit. But please don't speak of n dimensions as if everyone should know what you are talking about.

For example, Tifft has proposed that time has three dimensions, and shows how this might help to interpret some evidence ih quantum physics. But because he is introducing a new and foreign concept, he must carefully define what each new dimension means. Otherwise, you will properly ask "What does that mean?" Undefined concepts can only be introduced if one is prepared to define them, and can only be taken seriously if they have some observable, testable physical consequences. -|Tom|-

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Like everyone else here using this board, your board, I value and respect you, your knowledge, your thoughts and information, and your opinions.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

This is not a personal Message Board, but the professional Board of Meta Research. And I was expressing a personal opinion, not dictating policy as a Meta Research Board member. That is what "IMO" means -- "in my opinion". If a policy violation occurs, you will hear about that from a Moderator, I am sure.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>I was under the impression that these boards were to express ideas and thoughts and to debate the issues in order to find answers and better our knowledge.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I agree.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>I wasn't aware that people were suppose to just bow down to what someone says is "THE WAY IT IS", if that is the case, then why even ask the question.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I do not approve of the authoritative approach to science either. Personally, I question everything. And note that I carefully explained the technical problem with the content of the post -- again. However, I raised the appropriateness issue because I felt (a) the discussion had gone badly wrong; and (b) no one was correcting it. From these two points I concluded that it was becoming an embarrassment to readers, who might be turned off by a rehash of such elementary points and the denial of them by some participants.

You are free to disagree. Perhaps we can ask for expressions of opinions by others. My fear is that there now may be no "others", having all been driven away by the discussion. But I'd be glad to hear that I am wrong about that.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Would you please clarify exactly what it is that you want from these boards.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Personally, I'd like to see constructive ideas flow freely. But that should involve a certain level of self-discipline. What's the use of talking about a concept that is undefined except perhaps in works of science fiction? What purpose does it serve if a step in someone's reasoning is "...and then a miracle occurs..." (a famous Sydney Harris cartoon). IMO, that just wastes everyone's time explaining why miracles are not a part of physics. Often, responders have provided citations, and these are sometimes ignored.

So the bottom line here is that you can probably express anything as a first-level idea. But when the response is of the form "read this..." rather than in the form of a written-out explanation, where should the burden then fall? I want correspondents to be informed so that their challenges are meaningful, whether right or wrong. I think it bad manors, if not worse, when someone's error is corrected repeatedly and that someone refuses to become better informed about the issue, choosing simply to continue repeating the error.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>I don't plan to participate any longer unless you can explain why you would, so viciously, attack someone for expressing an opinion.<img src=icon_smile_angry.gif border=0 align=middle><hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I apologize that my choice of words came across as a "vicious attack". My intention was no worse than to express a mild annoyance that the previous several attempts to inform about this issue by me and others had been rejected. I felt, and still feel, that those who think otherwise (about the technical issue) have an obligation to inform themselves. After all, no one is paying tuition, so there should be limits on throwing the burden to educate back on the professionals and failing to do any homework. <img src=icon_smile.gif border=0 align=middle>

To make the point clearer by exaggeration, suppose someone claimed that (-2)^2 = -4. This is wrong because (-2)^2 = 4. However, if someone claims the former here, whose burden is it to correct and/or explain the error to the claimant? And won't any attempt to correct it in a few words seem to the claimant like an authoritative approach? Moreover, if someone did attempt to explain the error, wouldn't that make the thread intolerably boring for everyone else who learned this in first-year algebra?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>I don't know what else someone would call "the square of the velocity of light" besides c^2 as in E=mc^2 unless, you have some other word which has not been defined.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

c^2 is "the square of the velocity of light". I agree with that, and never said otherwise. But c^2 is <b>not</b> a speed, and it is not 299,792^2. (The units are part of the value.) As E=mc^2 implies, c^2 is an energy per unit mass, and has dimensions of energy per unit mass. Energy is not a speed, just as area is not a length.

Anyway, it is definitely not my wish that you or anyone should leave the Board. You all make interesting contributions from time to time. And I'm not laying down any new rules. I simply request that you (and everyone) keep in mind that many of us do not have time to engage in detailed discussions of elementary points. So please accept responses of the form "read this..." or "get better informed about that..." Does that answer work for you? -|Tom|-

Getting back to the train moving at the speed of light and then moving within at light speed from the front to the back would you be then at C minus C? And moving forward at C+C speed? And so moving forward requires much more effort.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>the speed limit is V (and I define it the following way because I could not find a teacher, friend or relative to teach me anything better):

V = magnitude(c^2) m/s

Where do you see the problem? If you can claim this is not right and prove it fine.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

This is not right. And that is because it assumes that c is a pure number without dimensions, and that is not the case. c is not 299,792,458. Instead,
c = 299,792,458 m/s = 299,792.458 km/s = 186,282 miles/s = 0.984 feet/nanosecond = 1 lightyear/year = 1/499 astronomical units/s = ... etc., etc. One can associate any number imaginable with c by a suitable choice of dimensions. And the squares of all these possible numbers are all different -- incompatibly different.

If one retains the dimensions as part of c when forming c^2, then one gets consistency because the dimensions are changed by the squaring process. But if the dimensions are removed and just a pure number is squared, then the result obviously depends on which of an unlimited set of pure numbers one can associate with "c" that one might choose to square. The result will be a random number, depending on this choice.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>(3e+^2 m/s = 9e+16 m/s<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Consider your example. Why did you square (3e+ [the cgs value of v] instead of (3e+5) [the MKS value of c] or 1.0 [the relativists' value of c] or 186,282 [the English value of c] or 0.984 [the geodicists' value of c] or 1/499 [the astronomers' value of c] or some other choice? Does nature somehow prefer MKS units? Or are all MKS units (such as the length of one meter and one second) purely arbitrary and man-made?

I think you know it is the latter. But that means the number in front of the units is equally arbitrary, and could be anything.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>It's been a pleasure to be on this boards and exchange ideas. My participation in any forum terminates when someone calls me stupid or idiot or uneducated. especially in a forum that claims to challenge conventional thinking... which this one does not.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

Speaking for myself, I always appreciate it when someone points out my errors, which I make with considerable frequency in life. And the earlier I get corrected, the better, because that keeps me from looking foolish in front of more people later when I might have repeated those errors.

So forgive me for treating you as I would wish to be treated in an analogous situation. In any case, let's not fight or be resentful, especially during this holiday season. There's way too much of that in the world now.

The best of the holidays to makis and everyone reading this Message Board! -|Tom|-

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>Getting back to the train moving at the speed of light and then moving within at light speed from the front to the back would you be then at C minus C? And moving forward at C+C speed? And so moving forward requires much more effort.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

In special relativity, ordinary matter moving at the speed of light or faster is impossible.

If the train were moving at a constant speed nearly (but not quite at) the speed of light relative to Earth observers, then anyone on the train would feel as if the train were at rest and the Earth was moving by at near the speed of light. So it would be equally easy for someone on the train to move in any direction. (This assumes no accelerations.)

If another train passed the first train at nearly the speed of light and headed in the same direction, the speed of that second train to an Earth observer is not nearly c+c. The speed is given by the law of addition for velocities which involves a square root and can never exceed c. This is all standard fare for students of relativity.

Without accelerations, no "extra effort" is involved. -|Tom|-

This is the view of GR with two trains but, Patrick's train is a single train with a person moving within. And adding C+C you get C anyway. The point is the effort is greater moving forward in his train than the effort needed to go the other way or C-C which gets to zero I guess. Patrick's train seems to be different than the GM train model having two trains moving in opposite directions. In either case we don't really know any of the above would in fact occur since we are not now able to do any of this stuff for real.