Light Cones / QM

**curiousphoton** · Nov3-09, 01:44 PM

I've always been interested and intrigued by the idea of light cones and how they fit in with other theories in physics. I have a couple of questions about them that I hope make sense are easily clarified:

(1) I understand why the shape of the Past Light Cone is a Cone. I don't understand how the Future Light Cone takes on a definite Cone Shape.

Wikipedia on Events outside of Light Cone:

"All other events are in the (absolute) elsewhere of E" (E being an Event occuring at the origin) "and are those that can not affect and can not be affected by E."

Example: A Light source emits a flash here on earth (Call this Event E). Looking at the Future Light Cone, a second later, Mars lies in the "absolute". The planet cannot affect or be affected by Event E.

But what about an electron. We can't say that a second later it lies in the absolute because QM tells us we can only know its future location to a certain probability. So technically it could affect E, but it lies outside the future light cone.

Any ideas?

**Fredrik** · Nov3-09, 03:14 PM

Special relativity is a classical theory, not a quantum theory. In SR, the motion of a particle is represented by a continuous curve in spacetime. You can take that to be the definition of a "particle" in all the classical theories.

Concepts such as "the light cone", "the causal future", "the chronological future", etc., are all concepts defined in the framework of classical SR. They are used in special relativistic QM too, because that theory uses the same model of space and time as classical SR, but they are defined relative to a point in spacetime, not relative to the position of an electron, which is never a point.

**curiousphoton** · Nov4-09, 01:21 PM

Originally Posted by Fredrik

Special relativity is a classical theory, not a quantum theory. In SR, the motion of a particle is represented by a continuous curve in spacetime. You can take that to be the definition of a "particle" in all the classical theories.

Concepts such as "the light cone", "the causal future", "the chronological future", etc., are all concepts defined in the framework of classical SR. They are used in special relativistic QM too, because that theory uses the same model of space and time as classical SR, but they are defined relative to a point in spacetime, not relative to the position of an electron, which is never a point.

I'm more confused now but thanks for trying. So are light cones real or not? You're saying it depends whether we are living in a SR world or QM world.

So in a SR world, the idea of a future light cone is real? If it is, I don't see how a electron or photon or particle can lie outside the future light cone...

**JesseM** · Nov4-09, 02:19 PM

Even in relativistic quantum theory it's possible to prove that quantum effects like entanglement and tunneling cannot be used to transmit information faster than light. So, the future light cone of an event E still represents all the points in spacetime that could possibly have access to information regarding E.

**curiousphoton** · Nov4-09, 03:01 PM

Originally Posted by JesseM

Even in relativistic quantum theory it's possible to prove that quantum effects like entanglement and tunneling cannot be used to transmit information faster than light. So, the future light cone of an event E still represents all the points in spacetime that could possibly have access to information regarding E.

Wait so quantum effects like entanglement and tunneling don't indicate faster than light information exchange? From everything I've read / heard, they do

**Ich** · Nov4-09, 03:49 PM

Well, you can read anything in the net. Not to mention this unspeakable Scientific American article where a philosopher and a teacher for creative writing (sorry, no joke) expose themselves.
So, finally, we come to the point where Wikipedia is more reliable than former scientific magazines. You won't find your position there. You'll find a "no communication theorem" instead.

**curiousphoton** · Nov4-09, 04:54 PM

Originally Posted by Ich

Well, you can read anything in the net. Not to mention this unspeakable Scientific American article where a philosopher and a teacher for creative writing (sorry, no joke) expose themselves.
So, finally, we come to the point where Wikipedia is more reliable than former scientific magazines. You won't find your position there. You'll find a "no communication theorem" instead.

So we seem to be getting way off topic...I thought the conflict between Relativitey and QM was well established and that everyone was looking for some sort of unified theory?

I assumed this fact in my original question. Is this not true?

**DrGreg** · Nov4-09, 05:26 PM

Originally Posted by curiousphoton

I thought the conflict between Relativitey and QM was well established and that everyone was looking for some sort of unified theory?

The conflict is between general relativity (with gravity) and quantum theory. There is no conflict between special relativity (without gravity) and quantum theory.

**pervect** · Nov4-09, 05:38 PM

There isn't any inconsistency between quantum field theory and special relativity. QFT is very well tested, having predicted the anomalous magnetic moment of the electron to about 10 decimal places, one of the most exact predictions in physics.

Loosely speaking, QM can be considered to be an approximation to QFT where particle creation and destruction is not allowed. QFT is more exact, but much more complex, so in applications where it's not needed, ordinary QM is used. Most such applications where QM is used rather than QFT (for instance, the Schrodinger equation) are non-relativistic, however.

For more, see http://en.wikipedia.org/w/index.php?...ldid=321777158

I believe there is some debate as to whether or not there is a fully relativistic quantum theory that is not a quantum field theory, but I'm not really positive about this, you'd have to ask someone else. But there isn't any problem at all with having a relativistic quantum field theory, in fact that's what the "standard model" of particle physics is.

BTW, QFT has a definite notion of causality it's sometimes called the "diamond property", that prohibits faster-than-light influences