Comments on: Contemplating Causality

By: Mark

Mark — Tue, 28 Oct 2008 13:47:58 +0000

Hi Moshe,

I’m not really an expert on this, but I think it depends how baroque a choice one is prepared to make for the Lagrangian. Defending such choices from, for example, an effective field theory point of view, is another matter.

By: Moshe

Moshe — Tue, 28 Oct 2008 12:56:34 +0000

Predictable knee jerk reaction to higher derivative theory is the following: the higher derivative terms become relevant only at sufficiently high energies, so anything that depends on their presence kicks in at sufficiently high energies. Therefore:

1. It should not observable at current energies.
2. By the time you get to those high energies, presumably of order the cutoff scale, you have no justification using any truncation of the low energy effective theory. For any reliable results you’d have to turn to the full underlying theory.

Any reason these generic words don’t apply to k-essence?

By: Mark

Mark — Tue, 28 Oct 2008 10:52:32 +0000

I meant the former David, although if you could make it work in some way …

By: David Moles

David Moles — Tue, 28 Oct 2008 08:57:09 +0000

When you say "the relevant theory may be fundamentally sick," do you mean fundamentally unwell, or fundamentally wicked awesome? 'Cause OMG a theory that allows superluminal propagation would be sick, yo.

By: Aaron F.

Aaron F. — Tue, 28 Oct 2008 05:09:17 +0000

Hey! I almost decided to drop in on one of those talks, just because the name of the workshop had “superluminal” in it. Homework won out in the end, but I’m glad the workshop was as interesting as it sounded!

By: James

James — Tue, 28 Oct 2008 02:48:28 +0000

“Spring forward, Fall back” – well got that wrong , but with complex, or, while we’re at it why not octionian, time, who cares about the direction, if it even exists?

By: James

James — Tue, 28 Oct 2008 02:42:59 +0000

OK,

So now I can add “complex time” to my list of unlikly ideas in this thread about causality/Qm fundamentals.

The clocks here in Europe just went back an hour – perhaps it should have been a rotation by exp(i * pi/3) ?

By: Lawrence B. Crowell

Lawrence B. Crowell — Tue, 28 Oct 2008 02:11:40 +0000

Yet in a funny way, if the universe tunnelled out of the vacuum state, or tunnelled trough a barrier then as with basic Schrodinger tunnelling of a particle the phase angle of the wave function in the barrier is imaginary. The notion that time might be complex valued is of course not considered, which is one reason why the idea is somewhat intriguing.

Lawrence B. Crowell

By: Mark

Mark — Tue, 28 Oct 2008 02:01:58 +0000

Imaginary time is used to demonstrate a formal equivalence between the path integral for quantum field theories and the partition function for thermal field theories, but isn’t something we think of as a physical time (and certainly not as complex).

By: Lawrence B. Crowell

Lawrence B. Crowell — Tue, 28 Oct 2008 01:53:14 +0000

The matter of causality strikes me as interesting with respect to what it is we mean by imaginary time. An imaginary phase may be seen as a case where the time becomes an imaginary time with t = hbar/kT. For a high temperature system this imaginary time is very small, but as temperature becomes small there is then more of this imaginary time available for the system to exist in an instanton or tunnelling states where this quantum behavior is detectable. We may then consider the imaginary time as analgous to the classical temperature, where for low real temperature the imaginary time assumes is analogous to a classical temperature that heats up material in the space plus imaginary time “spacetime.” Thus time in general might then be a complex valued vector, where ordinary time lies on the real axis of the Argand plane and temperature on the imaginary axis. For a low enough of a standard temperature the imaginary time as an internal temperature will act to heat up the quantum states of the system and they will then exhibit a phase transition or “melting,” which results in a fluid behavior that is scale invariant. Thus time and causality might be a certain phase state of the world which was established in the big bang or during inflation.

As for negative particles mentioned above, I have often wondered if there was much to be gained from modelling tachyons and other quirky particles as tiny Alcubierre warp drive spacetimes. These are negative energy spacetimes, or that violate the averaged weak energy condition. Generally of course we want these things to “go away” or to vanish in some way so that there are useful constraints on a theory.

Lawrence B. Crowell