Mathematical Obscurities in Special Relativity

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by kc3mx</i>
[brThe anwser depends upon what you think time is. This is not at all a question which can be glibly answered as many textbooks like to do. Now of course, the same problem applies for space. We don't know what it is either.
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I believe that clocks "generate" time and that all things that move are "clocks". If we have atomic clocks slowing down in a strong gravity field and pendulum clocks speeding up in the same strong gravity field, we’ve got atomic time slowing down and moving-mass time speeding up. Two different kinds of “time”, governed by two different laws of physics. One is quantum mechanics and “electrodynamical”, while the other is Newtonian mechanics.

I believe there is no “time” without motion. Stop all motion in the universe and you stop all time. Time is not something that “flows” as a mysterious invisible entity. It is something that transpires as a result of motion. It is a sequential numerical counting of cause and effect “events”. What creates the time and the sequence of events is the motion.

In my humble opinion.

David, I may have missed it; how do you know atomic clocks slow down in a magnetic field? Is there an equation for this process? Why is it said atomic clocks are very accurate if they are effected by all kinds of forces?

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Jim</i>
<br />David, I may have missed it; how do you know atomic clocks slow down in a magnetic field? <hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">


They slow down in a strong gravity field. They speed up in a weak field. The US gov averages several atomic clocks and calculates an average time based on a sea level position of an ideal master atomic clock.

Your interpretation is basically the same as adopted by Einstein. He asserts that clocks are time. This is a peculiar assertion, because it makes the measurement procedure the phenomena that is measured. This is illogical. My favorite example is the story that when Magellan's crew returned from their circum-navigation of the earth, they discovered that they were one day younger than their stay at home friends. This is an old version of the twins paradox. By the clocks of the stay at home friends the around the world trip took a day longer than by the clocks on Magellan's ships. So the trip around the world caused them to age more slowly than the friends who stayed at home.

I don't think that that clocks can be used to prove that time has changed its fundamental rate. Clocks measure time relative to a standard clock which is the definition of time in physics. But this definition of time is a device to formulate laws of physics in terms of the definition related to the standard. When a moving clock or a clock in a gravitational field slows down, does this mean time slowed, or that the physical process for the measurement of time has changed so that the clocks are no longer calibrated to the standard for time? I think the later conclusion is the only interpretation that is logically valid.

When a clock runs slow because the ambient temperature changes, we don't conclude that heat caused time to change, we conclude that heat changed the physical process by which time is measured and that the clock no longer correctly measures time relative to the time standard.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by kc3mx</i>
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When a clock runs slow because the ambient temperature changes, we don't conclude that heat caused time to change, we conclude that heat changed the physical process by which time is measured and that the clock no longer correctly measures time relative to the time standard.
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My daffodils are their own thermodynamic clocks. Their growth speeds up in the spring when the weather turns warm. It slows down if the weather turns cold again. This is a biological thermodynamic-chemical clock. Well insulated atomic clocks in the same place don’t shift for thermodynamic reasons. Daffodils moved to sea level still are regulated by thermodynamic time, not atomic time. There are different kinds of time, depending on the various laws of physics and the various kinds of clocks (i.e. the various kinds of motion and physical action).

Any “time standard” is usually represented by just a “steady clock”. This is an “ideal” situation in which some clock, of any kind, never changes rates, but I don’t think the “ideal” is ever realized in nature. It doesn’t matter what kind it is, but atomic clocks seem to be the most steady on earth.

My hypothesis differs from Einstein in that he thought all of “time” slowed down and speeded up at the same rate, for all kinds of clocks, but with atomic clocks becoming his own personal favorite. I can’t see in his papers that he ever understood the concept of thermodynamic time or the fact that it ran at different rates from atomic time.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by kc3mx</i>
<br />they discovered that they were one day younger than their stay at home friends.
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I hate when that happens.