“What we observe as material bodies and forces are nothing but shapes and variations in the structure of space.”

— Erwin Schrödinger (via mysteriousquantumphysics)

Physics Blog
All about Physics

“What we observe as material bodies and forces are nothing but shapes and variations in the structure of space.”

— Erwin Schrödinger (via mysteriousquantumphysics)

“Inflation may give us an enormously huge number of Universes that reside within a greater multiverse, but there simply aren’t enough of them to create an alternate, parallel you. The number of possible outcomes simply increases too fast for even an inflationary Universe to contain them all.

In all the multiverse, there is likely only one you. You must make this Universe count, as there is no alternate version of you. Take the dream job. Stand up for yourself. Navigate through the difficulties with no regrets, and go all-out every day of your life. There is no other Universe where this version of you exists, and no future awaiting you other than the one you live into reality. Make it count.”

Our observable Universe, as vast and enormous as it may be, is still finite. There are a finite number of galaxies containing a finite number of atoms and particles that have existed for a finite amount of time since the Big Bang. There’s an idea in quantum physics call the many-worlds interpretation, where all the various quantum outcomes that are possible actually do occur, but they simply occur in parallel Universes: where the Universe was identical to our own until a critical moment when a particular quantum decision occurred.

“But the motivation for quantizing the field is more fundamental than that the argument between those favoring perturbative or non-perturbative approaches. You need a quantum field theory to successfully describe the interactions between not merely particles and particle or particles and fields, but between fields and fields as well. With quantum field theory and further advances in their applications, everything from photon-photon scattering to the strong nuclear force was now explicable.”

What’s wrong with quantum mechanics? It might surprise you to hear that the answer is, “it isn’t quantum enough.” The enormous differences between the quantum and the non-quantum Universe are so striking, as we replace:

* continuous matter with discrete particles,

* ideal points with dual-nature wave/particle quanta,

* and observable properties like position and momentum with quantum mechanical operators containing an inherent uncertainty.

But it’s still not enough. For one, the original (Schroedinger) equation of quantum mechanics doesn’t play nice with relativity, but even the relativistically invariant versions don’t describe reality fully. Why not? Because only the particles are quantized in quantum mechanics. To reveal the full behavior, you need to quantize their fields and interactions, too.

“Now, think about what would be required to do today to tear down one of our leading scientific theories. It’s not as complicated as you might imagine: all it would take is a single observation of any phenomenon that contradicted the Big Bang’s predictions. Within the context of General Relativity, if you could find a theoretical consequence of the Big Bang that didn’t match up with our observations, we’d truly be in store for a revolution.

But here’s the important part: that won’t mean that everything about the Big Bang is wrong. General Relativity didn’t mean everything about Newtonian gravity was wrong; it simply exposed the limit of where and how Newtonian gravity was successful. It will still be accurate to describe the Universe as having originated from a hot, dense, expanding state; it will still be accurate to describe our observable Universe as being many billions of years old (but not infinite in age); it will still be accurate to talk about the first stars and galaxies, the first neutral atoms, and the first stable atomic nuclei.”

There are a great many people out there who absolutely cannot wait for the day where one of our greatest scientific theories is demonstrated to be wrong. Where an experiment or observation comes in that cannot be reconciled with our leading ideas of how the Universe works. At last, perhaps an unintuitive part of our existence, like relativity or quantum mechanics, might be replaced with something that’s a closer approximation of our actual reality. But that won’t invalidate what we already know; it will merely extend it.

“Now, think about what would be required to do today to tear down one of our leading scientific theories. It’s not as complicated as you might imagine: all it would take is a single observation of any phenomenon that contradicted the Big Bang’s predictions. Within the context of General Relativity, if you could find a theoretical consequence of the Big Bang that didn’t match up with our observations, we’d truly be in store for a revolution.

But here’s the important part: that won’t mean that everything about the Big Bang is wrong. General Relativity didn’t mean everything about Newtonian gravity was wrong; it simply exposed the limit of where and how Newtonian gravity was successful. It will still be accurate to describe the Universe as having originated from a hot, dense, expanding state; it will still be accurate to describe our observable Universe as being many billions of years old (but not infinite in age); it will still be accurate to talk about the first stars and galaxies, the first neutral atoms, and the first stable atomic nuclei.”

There are a great many people out there who absolutely cannot wait for the day where one of our greatest scientific theories is demonstrated to be wrong. Where an experiment or observation comes in that cannot be reconciled with our leading ideas of how the Universe works. At last, perhaps an unintuitive part of our existence, like relativity or quantum mechanics, might be replaced with something that’s a closer approximation of our actual reality. But that won’t invalidate what we already know; it will merely extend it.

“Quantum mechanics is one of the most philosophically profound and counterintuitive ideas that humanity has ever encountered. It has stood the test of time not because of its beauty, elegance, or the compelling nature of the theory, but rather because its results agree with experiment. Quantum physics was only reluctantly embraced by a great many scientists because of how divorced its rules are not only from our own experience, but of one of the great ideas of science: that we can learn the rules of nature to make accurate predictions about our own future. There’s a fundamental limit to our predictive ability, and quantum physics is what dictates that limit.

It is not the job of physics to make you comfortable with the Universe; its role is to describe reality. In that, quantum physics is an unparalleled success. But philosophically, what Bohr said all those years ago, ‘Anyone who is not shocked by quantum theory has not understood it,’ is still true.”

Quantum physics is weird. Part of why it met with such resistance is that it’s so divorced from our normal experience, and so counterintuitive as far as what it predicts. This was illustrated beautifully by the Einstein-Podolsky-Rosen (EPR) paradox, which appeared to show a contradiction: two entangled particles, separated by great distances, appeared to ‘know’ whether the other one was measured or not, at least as far as statistical outcomes go. Yet that would result in a transmission of information faster-than-light, a no-go in relativity.

Well, that paradox is only a true paradox if you apply classical laws to the Universe. Bell’s inequality, developed in the 1960s, showed that there’s a difference between what quantum mechanics predicts and what a theory of local, hidden, deterministic variables predicts.

“If you accept that inflation is a stage that occurred in the Universe’s past prior to the hot Big Bang, and that the Universe itself is inherently quantum in nature, the existence of a multiverse is unavoidable. Even though we cannot observe these other Universes, we can observe a huge amount of evidence for inflation, indirectly pointing to its inevitability. We can also observe a huge amount of evidence that the Universe itself is quantum, even though we have no proof that inflation itself behaves as a quantum field. If you put these pieces together, it unambiguously leads to the prediction that our Universe should be only one of countlessly many Universes, all embedded in an eternally inflating, expanding background. One Universe is not enough. Even though we cannot detect it, the prediction of a multiverse is unavoidable.”

When Carl Sagan’s Cosmos began, the first words you heard were, “The cosmos is all there is, or was, or will be.” Only… what if it weren’t? What if what we know as our cosmos, i.e., the entire Universe, were only one of countlessly many, all embedded in a strange spacetime that was continuously creating more of them? This sounds like some sort of strange speculation, but it’s actually an unavoidable consequence of two of our best theories put together: cosmic inflation and quantum physics. Combine them, and you get a multiverse.

In linear algebra, an

eigenvectorof a linear transformation is a non-zero vector

that only changes by a scalar factor (itseigenvalue) when that linear transformation is

applied to it.

Now* for the sake of simplicity* lets assume that Energy* as a linear transformation, and when it acts on some position (x1,x2) gives you the energy at that point (e0).

(x1,x2) – Eigenvector, e0 – Eigenvalue.

This e0 that you get is a physical measurable quantity and you do not want this value to be complex. Why ? Complex energies are not a thing of the real world.

And the reason why Hermitian matrices are important in Physics is because if a Matrix is hermitian, then it has real eigenvalues.

Thanks for asking!

* It need not be Energy, it could be any physically measurable quantity. We have just taken energy as an example here.

** A Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose ( A = A ^{†} )

[1] Why on earth is matrix multiplication NOT commutative ? – An Intuition

You might have seen animations like this that show an electron undergoing a transition from a lower energy to a higher energy state and vice versa like so:

There is something really important about this image that one must understand clearly.

The diagram represents the transition in *energy *of an electron BUT this does not mean that the electron

is magically jumping from one position and respawning at another

position.

* The electron’s position is NOT doing this i*

If you want to know about the probability of finding an electron around the nucleus at a certain energy level, you look at its wavefunction and not at the energy diagram.

Here is the wavefunction of a hydrogen atom and each stationary state defines a specific energy

level of the atom.

This might not sound like a big deal but one might be surprised to know that there are a lot of people who think that the electron is magically transported from energy level to another which most certainly is not true.

Have a good one!

– A2A