Paradoxes and Dilemmas

tvanflandern
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22 years 6 days ago #4023 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[Patrick]: Rather then saying accelerated, what I should have said here is that the traveling twin is traveling at a *SPEED* much greater then the Earth twin which would appear to the traveling twin that the other has slowed.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

But no two observers with a relative speed can tell which is really moving and which is at rest, according to SR.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>What slows time is either an increase in speed (acceleration) or an increase in gravity.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Nope. In SR, what slows time is relative speed. If the speed difference changes, so does the amount of the time changes -- both rate and time slippage. But you don't need any change in speed -- ever -- to get the basic effect.

Likewise for gravity. Entering a stronger gravitational force does nothing to time, just as acceleration does nothing to time. Entering a stronger gravitational potential changes the rate of clocks just as a larger relative speed changes clocks.

These are separate concepts. Either force/acceleration or potential/speed can be changed at some particular place and time without a change in the other. -|Tom|-

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tvanflandern
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22 years 6 days ago #3871 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Combining the above apparently true statements, I may conclude that the SR twin paradox to be true requires the creation of a gravity potential in the frame of the travelling twin that will slow time in such a rate as to outpace by large the increase in clock rate due to speed.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Both effects, speed and potential, slow clocks. These normally accumulate, as my on-line presentation showed.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>If such a potential cannot be present, SR is invalid both logically and in reality. Slippage cannot have frame preference unless absolute time is invoked.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

In SR, the situation is just the opposite of what you describe. SR is internally consistent, and does not allow absolute time (or space) to exist. The key is "time slippage", whereby clocks in the moving frame tick slower, but frame-time elapses faster. The past and future are both present *now* in any frame with a relative motion.

The paradox resolution is highly non-intuitive, but perfectly logical (in the mathematical sense). It just does violence to your usual understanding of the nature of time, and therefore to reasoning (such as yours above) based on that understanding. -|Tom|-

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AgoraBasta
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22 years 6 days ago #3872 by AgoraBasta

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<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Either force/acceleration or potential/speed can be changed at some particular place and time without a change in the other. -|Tom|-<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>Tom,

Would you agree that uniqueness theorem for the force/potential relation does not stand?

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tvanflandern
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22 years 6 days ago #4025 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Would you agree that uniqueness theorem for the force/potential relation does not stand?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

What theorem is that? Force is the gradient of potential, but that is a mathematical relationship, not a physical one. A gradient is just a type of derivative. So the relation of force to potential is like that of acceleration to velocity. Obviously, the physical causes and properties of acceleration and velocity can be quite different. Likewise for gravitational force and potential. -|Tom|-

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tvanflandern
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22 years 6 days ago #3873 by tvanflandern

Replied by tvanflandern on topic Reply from Tom Van Flandern

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>[Patrick]: Are you saying that the speed of gravity(c^2) is faster then the speed of light(c)?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

c^2 is not, and cannot be, a speed. Besides, c^2 can be greater than, equal to, or less than c depending on choice of units. Why do you deny the legitimacy of assigning c = 1? [E.g. The speed of light is one light-second per second, or one light-year oer year.] Units of meters per second are arbirtary, man-made units with no physical significance.

Nothing I said in this thread relates to the speed of gravity.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>So..., 2 travelers: 1 travels at the speed of light(c) the other travels at the speed of gravity(c^2) the gravity traveling twin ages less then the light traveling twin?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

Given c = speed of light and s = speed of gravity, then experiments indicate that s >> c. Specifically, s > 20,000,000,000 c. But this has nothing to do with SR or the twins paradox. Nothing can travel faster than c in forward time in the theory of special relativity (SR).

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote> 2) What is time past c?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

The question does not make sense to me. Please study the subject of "dimensions" in physics. To be compared, two things must have the same types of dimensions (e.g., powers of length, time, mass). Dimension units are arbitrary.

<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>3) Do you have different classifcations of gravity? (ie "pushing" "pulling")<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

See the book Pushing Gravity. -|Tom|-

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AgoraBasta
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22 years 6 days ago #4026 by AgoraBasta

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<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>
<BLOCKQUOTE id=quote>quote:<hr height=1 noshade id=quote>Would you agree that uniqueness theorem for the force/potential relation does not stand?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote>

What theorem is that? <hr height=1 noshade id=quote></BLOCKQUOTE id=quote>
That's about the unique potential solution existing for a given force field and boundary conditions.
I think this lauded theorem is plain wrong. Here's why -

Trivial calculations prove that, arbitrary modification of any existing force/potential solution is a spatial area of lower dimensionality than that of the solution, delivers a solution just as valid. This is absolutely correct if modification area doesn't have common points with the boundary. When intersection with the boundary is desired for a modification area, the same considerations may be applied to the area of modification - i.e. as long as intersection of the boundary with the area of modification is of lower dimensionality than that of both boundary and the area of modification, the modification can be nearly smoothly extended beyond the boundary (by "writedown" of an area of yet smaller dimensionality from the area of modification). Such or similar considerations may be applied to any attempt of proof of any relevant "uniqueness theorem" out there and are a fundamental limitation of applicability of such theorems. 

(I quote myself from a thread at another BB www.badastronomy.com/phpBB/viewtopic.php...133&forum=2&start=75 )

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