My little tribute to Irving Segal: Simultaneity breaks down

J. G. Waller · science forum beginner Joined: 13 Apr 2006 Posts: 12

Imagine you have a friend, Irving, living in a planet, 8 light-years
apart, and you live in New York City. The question is, does Irving
exist when you exist?. I say, if you can communicate some information
to him, are you sure he exists when you send the message to him?.
Perhaps he only exists when the message is received, not before,
neither sooner nor later. How can you prove that your friend exists
when you send your message to him?. Is he alive in that moment?.
You can argue you may receive a reply, at least, in 16 years in your
future, so you will have known then your friend existed when you sent
your message to him. But, that's wrong, that only proves that your
friend existed 8 years ago, when he received your message. Notice that
you need your time to run for knowing about your friend's existence.
You need to wait, at least, some information travelling at speed of
light, and it is equivalent to say, you need to wait time to run, in
order your friend can exist in your spacetime reference frame. Why
can't information travel faster than light?. The answer seems now to
be easy: you can't comunicate anything to someone who does not exist
yet in your proper time. You exist in a past time of your friend's
proper time, and your friend exists in a past time of your proper
time. The constancy of speed of light in the vacuum is then the
evidence that simultaneous events are not possible in our physical
real world!.Light emitted by you can be regarded as something that
is left stationary in your time, like a label, meanwhile you advance
towards your future.

If this counterintuitive idea is true, then we need to revise some
standard assumptions, namely Minkowsky spacetime topology, lorentz
transformations, special relativity theory, and so on. My intuition
tells me this idea is true.

A suitable solution for the spacetime topology would be a relative
expanding 3-sphere, with current radius R, in which light can
propagates in tangential euclidean null geodesics to the source-event.
So, what we call, under standard assumptions, the light-cone in a
Minkowsky spacetime, would be spanned now to an euclidean spacetime
manifold tangential to the event (R,0,0,0). This model would preserve
what we call causality of events, it is saying that if an event is
cause of other event, then the former always precedes in time to the
latter, regardless the reference frame from which they are considered.

Let us see how could be a revision of standard lorentz transformations,
which could preserve causality of events. Suppose now, your friend
Irving is moving at a non null speed v towards you, at that distance r
of 8 light-years. In order to compute a more accurate relativistic
boost than the standard one, we would need to sum two phases, one, f_1,
related to speed v, and another, f_2, related to distance r, regarded
as equivalent to a recession speed, v_r. Both two phases would conform
a sum phase f, arising an extended new lorentz transformation,
such as this:

f_1 = arcsin(v/c)
f_2 = arcsin(v_r/c)
f = f_1 + f_2

Notice that the recession speed v_r, considered here, is not a
kinematical speed, but the relativistic contribution of the distance
r, and it is always a positive real value, because negative space-like
distances have no physical meaning. So the new gamma factor for a
lorentz transformation would be:

gamma = 1/cos(f),

and the distance r that light has travelled would be:

r = R(tan(f)),

where R is the radius of the 3-sphere when the message was sent.

There are still serious cosmological discrepancies and discussions
about what causes recession speeds, how they are interpreted, and
whether they are addressed by linear or quadratic functions of r.
Regardless the form it could finally take, my intention here was
only to show how the light-cone in a minkowskian spacetime must be
spanned to a complete tangential 3-D euclidean space, in order to
preserve causality of events, yielding a new model for topology of
spacetime.

This was my little and modest tribute to Irving Ezra Segal,
mentor of John Baez (http://math.ucr.edu/home/baez/segal.html).
Segal's Chronometric Cosmology was misunderstood and sadly
underestimated, but it deserves more serious attentions, because
its theoretical core is the key which will unlock doors to
Quantum Gravity.

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