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From: "Paul.B.Andersen" <relativity@paulba.no>
Newsgroups: sci.physics.relativity
Subject: Re: Humans can't observe time. Even less, the pass of time. Science
 is an illusion.
Date: Fri, 25 Apr 2025 20:54:41 +0200
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Den 25.04.2025 00:13, skrev gharnagel:
> On Thu, 24 Apr 2025 8:21:30 +0000, Paul.B.Andersen wrote:
>>
>>
>> In physics "time" is a well defined, measurable entity.
>>
>> https://paulba.no/pdf/Clock_rate.pdf

> 
> Just because we can measure it doesn't mean we understand it.

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.

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.

> 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.

Relativity (SR/GR) does obviously not "explain" anything.
But SR/GR will correctly predict what the different observers
will measure in experiments.

If you think it is self-contradictory that different observers
have different measurements of the observed object's properties,
consider this:

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.

> 
> 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.

This is nonsense.


Let "the moving object" be a clock.
The metric in flat spacetime can be written:

    dτ² = dt² - (dx² + dy² + dz²)/c²   (1)

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.

from (1) we have:
   (dτ/dt)² = (1 - ((dx/dt)²+(dy/dt)²+(dz/dt)²)/c²) = (1−v²/c²) (2)

where v = √((dx/dt)²+(dy/dt)²+(dz/dt)²) is the magnitude of
the moving object's velocity.

from (2) we have:
  dt/dτ = 1/√(1 − v²/c²) =  γ

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

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

If v = 0, the object is stationary and γ = 1.
U₀ = 1, U₁ = 0, U₂ = 0, U₃ = 0

So the "rate of the clock along the time axis" is 1.

That does _not_ mean that the clock is moving at the speed
of light along the  time axis (what a weird idea ).

It simply means that the clock is ticking at its normal
rate, one time unit per time unit.

The four "dimensions" are _not_ identical, the temporal "dimension"
is fundamentally different from the spatial "dimensions".


It can be shown that the magnitude of th four-velocity is invariant:

  U = - U₀² + U₁² + U₂² + U₃² = -1

> 
> 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.
> 
> One idea is that time reversal would be a tough problem for
> causality.


-- 
Paul

https://paulba.no/