Why no tensors in quantum mechanics?

Benjamin Schulz

cfgauss wrote:

> Now, it seems like we could form another "quantum
> mechanical field tensor" in terms of the components of A and B, just
> like we did for E and B, and re-write our differential equations as
> tensor equations like we did before, and do more relativity-stuff.
> Now, it seems to me that since we've got something in the tensor
> language of general relativity, we should be able to do general
> relativity with this. But, obviously, we can't, or people would be
> doing this. Why don't we do this (or do we, and no one has told me
> about it)? At what point does this break and not make any sense
> anymore?

The Correspondence Principle from which operators are formed, does per
definition only hold in Cartesian Coordinates. For example, you could
write an Hamiltionian in spherical coordinates. If you want to put the
definitions of the momentum operator, you get the wrong hamiltonian,
even if the space is the same. Simply by definition you must start with
cartesian coordinates, putting in your operators and then making the
conversion to other coordinates. When the operators are only defined for
a special space with metric, then this is so, with the whole
schroedinger equations and its solutions. A way beyond this, are path
integrals, for example, which one can try to formulate for other
metrics.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.

mikem@despammed.com

Jeremy Price wrote:

> We can write Psi in terms of real and
> imaginary parts, say Psi = A + i B.
> [...]
> Can we at least do relativistic quantum
> mechanics like this if we wanted to?

I can't think why you'd want to. The
probability density involves Psi* Psi
which means both A^2 and B^2 contribute
to the experimentally-meaningful
probability. I doubt there's much
value in separating the two things the
way you suggest.

As for QM and relativity, look in your
nearest physics library for a book
on relativistic QM, which will tell you
about the Klein-Gordon equation and
Dirac equation. Then take a look at
full-on quantum field theory. These
theories are compatible with special
relativity. General relativity is
another matter though.