On Fri, 25 Apr 2025 18:54:41 +0000, Paul.B.Andersen wrote:
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Den 25.04.2025 00:13, skrev gharnagel:
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On Thu, 24 Apr 2025 8:21:30 +0000, Paul.B.Andersen wrote:
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In physics "time" is a well defined, measurable entity.
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https://paulba.no/pdf/Clock_rate.pdf
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Just because we can measure it doesn't mean we understand it.
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You can't 'understand' why Nature works as she does.
A theory of physics is a mathematical model of an aspect of Nature.
It doesn't 'explain' anything.
I believe you are "misunderstanding" me. It is possible to under-
stand why a theory works when you have experimental evidence for
the inputs to that theory. For SR we have the principle of rela-
tivity, the constancy of the speed of light, etc. Application of
those postulates (i.e., determined by measurements) allows us to
understand why time dilation happens. We don't understand why
the principles exist -- at present. We may someday, but those
will be based on some other measurements that we don't understand
why nature works that way.
The only test of a mathematical consistent theory is if it can
correctly predict what will be measured in experiments.
It takes but one wrong prediction to falsify a theory.
Of course, but that one wrong prediction must be a GOOD prediction,
not one invented by an incompetent. And if it turns out to BE a
good prediction, it will likely be based on different postulates.
Same with a good measurement.
And when we measure it, and different observers disagree with
our measurement, and relativity "explains" the disagreement,
might not really bring us closer to understanding it.
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Relativity (SR/GR) does obviously not "explain" anything.
But SR/GR will correctly predict what the different observers
will measure in experiments.
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If you think it is self-contradictory that different observers
have different measurements of the observed object's properties,
consider this:
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The observer's state of motion can not affect the observed object.
But the observer's state of motion can affect the observer's
measurements of the observed object's properties.
Again, you misunderstand me. You are preaching to the choir.
I attended a lecture many years ago where it was explained that
each of the four dimensions were really identical and we were
always moving at the speed of light - along one of them. That
one was our time dimension. That seemed to be very satisfying
at the time. This would mean that there is a basic symmetry
between time and space.
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This is nonsense.
No, it's not (but I disagree with it)
To play devil's advocate, what that lecturer said is EXACTLY what
the Minkowski diagram shows: The stationary observer begins at
x = 0 and t = 0, but he doesn't STAY at t = 0. He is moving at a
constant rate along the t-axis. Usually, the t and x-axes have
the same scales (note: the speed of light is depicted at a 45 degree
angle). Can you tell how fast he's moving along the t axis?
Let "the moving object" be a clock.
The metric in flat spacetime can be written:
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dτ² = dt² - (dx² + dy² + dz²)/c² (1)
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where τ is what the clock shows, c is the speed of light
and t,x,y,z are the coordinates of an inertial frame of reference.
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from (1) we have:
(dτ/dt)² = (1 - ((dx/dt)²+(dy/dt)²+(dz/dt)²)/c²) = (1−v²/c²) (2)
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where v = √((dx/dt)²+(dy/dt)²+(dz/dt)²) is the magnitude of
the moving object's velocity.
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from (2) we have:
dt/dτ = 1/√(1 − v²/c²) = γ
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Let the velocity of the clock be:
v₁ = dx/dt component along x-axis
v₂ = dy/dt component along y-axis
v₃ = dz/dt component along z-axis
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The components of the four-velocity will be:
U₀ = dt/dτ = γ component along the time axis
U₁ = dx/dτ = (dx/dt)⋅(dt/dτ) = γ⋅v₁ component along the x-axis
U₂ = dy/dτ = (dy/dt)⋅(dt/dτ) = γ⋅v₂ component along the y-axis
U₃ = dx/dτ = (dz/dt)⋅(dt/dτ) = γ⋅v₃ component along the z-axis
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If v = 0, the object is stationary and γ = 1.
U₀ = 1, U₁ = 0, U₂ = 0, U₃ = 0
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So the "rate of the clock along the time axis" is 1.
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That does _not_ mean that the clock is moving at the speed
of light along the time axis (what a weird idea ).
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It simply means that the clock is ticking at its normal
rate, one time unit per time unit.
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The four "dimensions" are _not_ identical, the temporal "dimension"
is fundamentally different from the spatial "dimensions".
Not on a Minkowski diagram. And your equations for four-velocity
have left out the "dimensions" of the dimensions: they aren't simply
v, they are v/c, so your dimensions are light-seconds/second, or
such.
It can be shown that the magnitude of th four-velocity is invariant:
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U[²] = - U₀² + U₁² + U₂² + U₃² = -1
Yes, and to the stationary observer, the speed of the clock along U₀
is no longer 1, it's shared with the speed along the spatial dimensions.
To the clock, however, it's happily moving along its t' axis - at speed
c.
To reiterate, I don't go along with time being another spatial
dimension,
even though the Minkowski diagram AND the Lorentz transform treat it
EXACTLY that way.
BTW, it has been shown the four-vector notation is invalid for tachyons
due to a nasty little error in the four-momentum derivation which nearly
everyone has missed.
Kapuscik, E., "On a Fatal Error in Tachyonic Physics," Intl. J. of
Theor. Phys., 54, pp. 4041-4045 (2013). DOI:10.1007/s10773-014-2458-1.
arXiv:1412.6010.
G. L. Harnagel, "Tachyons, the Four-Momentum Formalism and
Simultaneity,"
Universal Journal of Physics and Application 17(1): 1-7, 2023
DOI: 10.13189/ujpa.2023.170101.
More recently, some cracks in that view have appeared due to
quantum mechanics. Vaccaro has published a couple of papers
about "Quantum asymmetry between time and space," (2016)
arXiv:1502.04012.
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One idea is that time reversal would be a tough problem for
causality.
Another is that mass-energy can be localized in space but not in time,
else mass-energy is not conserved.
So I totally agree with you, Paul, that time is NOT a spatial dimension.
This means that using certain formalisms may bite you in the behind if
you're not careful.
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