B Is the Universe grainy below the Planck Scale?

[CrackerMcGinger]

What is quantum gravity and how do you calculate the probability of where the particle is? I probably phrased the second half of that question wrong.

 

[jfizzix]

Quantum gravity, or a quantum theory of gravity is a theoretical description of how gravity works at the small scale of, for example, elementary particles.
Currently, there are multiple theories being worked on that might do this.
So far, no theory of quantum gravity has been backed up or falsified by experiment, so more work remains to be done.

If you have a quantum particle, the probability density of where it is is described as the square of the magnitude of its position wavefunction.
To find the probability that it is in a given box of space, you integrate the probability density over the region of space given by the box.

 

[CrackerMcGinger]

If you have a quantum particle, the probability density of where it is is described as the square of the magnitude of its position wavefunction.
To find the probability that it is in a given box of space, you integrate the probability density over the region of space given by the box.

Can you explain this in simpler terms and possibly give a specified example?

 

[jfizzix]

Probability density is probability per unit volume (or unit length in one dimension).

If the probability density is constant, then the total probability is equal to the probability density times the total volume.
If the probability density is not constant, then we break up the total volume into small pieces, where the probability density is nearly constant in each piece.
Since the probability density is constant in each piece, we can find the probability for each piece, which is the density times the volume for the piece.
By adding up the probabilities to be within each of these pieces, we get the total probability to be in the total volume V.
This sort of operation is called integration, and is something you'll see in calculus.

 

[CrackerMcGinger]

And now is the time that I realize that I won't understand this completely until I take calculus in two years. But, and I only ask this because I am extremely interested in this, could you express this in terms so that a person who is taking geometry could understand. Now I am starting to understand better, but the terms are still going over my head.

 

[naima]

What is quantum gravity and how do you calculate the probability of where the particle is? I probably phrased the second half of that question wrong.

I think that QG is about probabibilities of metrics not of particles.
take a spin network in lqg. Have you a probability to find a particle at each node?

 

[enorbet]

I'm rather fond of Lee Smolin's work because although he has been heavily invested in many aspects of the search for a coherent explanation for QG (His "Three Roads to Quantum Gravity" is still instructive on that quest and understandable in large part without post-Calculus Math) he is one of the few who have directly addressed the repeated experimental results from ESA's Integral gamma ray observatory and it's implications that if Gravity is Quantized, if the Universe is "grainy", then it must be at orders of magnitude smaller than Planck Scale, 10^-48 m or smaller.

I recommend his books and lectures even though his recent application of Evolution on a Universal Scale is highly controversial. For more on the ESA Integral evidence you may start here ====>>>

http://www.esa.int/Our_Activities/Space_Science/Integral_challenges_physics_beyond_Einstein

 

[jfizzix]

And now is the time that I realize that I won't understand this completely until I take calculus in two years. But, and I only ask this because I am extremely interested in this, could you express this in terms so that a person who is taking geometry could understand. Now I am starting to understand better, but the terms are still going over my head.

Imagine space.
Now, imagine you place a really fine grid on that space where the squares are so small that nothing really changes in each square.
Next, imagine a particle in that space with a wavefunction.
The wavefunction is a mathematical object that completely describes the state of the particle. This is one of the things you assume in quantum theory (i.e., that a particle has a wavefunction that describes its state)
The wavefunction will be about constant in each square of the grid since the squares are small enough.
The probability for the particle to be in each square of space is related to the square of the magnitude of the wavefunction within this square. This is another one of the things you need to assume in quantum theory (it's called Born's rule).
To find the probability for a particle to be in a given region of space, add up the probabilities to be in each square inside the region.

Just to be clear, the wavefunction tells you more than just the position probabilities. You can take the magnitude square of it to get them, but you can do more too. You can also transform the wavefunction into a different coordinate system so that its magnitude square gives momentum probabilities instead. Since you can't get the momentum probabilities from the position probabilities, the wavefunction must contain more info.

 

[ddd123]

he is one of the few who have directly addressed the repeated experimental results from ESA's Integral gamma ray observatory and it's implications that if Gravity is Quantized, if the Universe is "grainy", then it must be at orders of magnitude smaller than Planck Scale, 10^-48 m or smaller.

What did he say? I can't find anything tbh.

 

[enorbet]

ping ddd123 - I'll have to find it again since I apparently didn't bookmark it but in a video lecture he recognized that a few branches of both String Theory and QG were effectively dead ends due to the size constraints apparent from Integral. Some saw it as defeatist but many, including me, saw it as adaptive and focused more on his message to encourage his students and anyone else working in theoretical physics and predictive mathematics to keep abreast of experimental developments, noting that we are in a kind of Golden Age for study in both the Macro and Micro worlds.

Brian Greene may posses a "beautiful mind" but I find Lee Smolin more scientific while still retaining creativity. His leaps are substantially smaller than many in the field and rarely confined to a "straight line" agenda.

 

[enorbet]

ping ddd123 - I'm still looking but as you may know Mr. Smolin is a prolific writer and speaker. The problem in finding just that one is like finding a needle in a stack of needles since it was/is not labeled "ESA", "Integral" or with any such cues. He is painfully aware of the deserved criticism of work so far in String Theory and QG (for over 30 years now) that there is no experimental observations even remotely construed as supporting evidence.

Many forms of String Theory work under the assumption that Strings are at Planck length and nothing smaller than that makes sense.

Most forms of Loop Quantum Gravity depend on Planck Area within a factor of 10, as the smallest possible area.

Since Mr. Smolin works in both these areas he is invested heavily in "graininess" at the Planck Scale. I'm sure his jaw dropped when he saw the Integral data, especially considering the great distance and energy of the GRB. Thankfully as in many of his lectures and even in his Ted Talk he vows his allegiance to a basic tenet of true Science, that of happily accepting failure. He seems to walk the walk as well as talk the talk. Many seem to choose to ignore such a profound observation and act as "business as usual".

His Darwinian approach may seem controversial to many but if it is even partially true that the Universe is at all "homogenous" we do observe Evolution as a natural consequence of self-ordering. responding to the same physical laws everywhere. That the Universe evolves doesn't seem a far-fetched concept in that light and certainly must be a productive avenue to explore, even if only for falsification.

I will continue looking for the original lecture but hopefully you are as well. It surely isn't wasted time.

 

[Prof_ Sun]

Please advise how to construct the wave function of graviton?

 

[bhobba]

Please advise how to construct the wave function of graviton?

QFT particles do not always have wave functions - this is one case - EM is another.

We do however have a QFT:
https://arxiv.org/abs/1209.3511

Beyond the Plank scale we don't know - yet.

We do not, and inherently can never know, if a gravitational field is like say an EM field and acts on things as if space-time is curved, or space-time is actually curved. The QFT description assumes the former.

Thanks
Bill

 

[Prof_ Sun]

thanks.

it is a nice paper, are you the author of the article:

The effective field theory treatment of quantum gravity

by Prof. John F. Donoghue

 

[bhobba]

it is a nice paper, are you the author of the article:

No.

Its just there is a bit of confusion about quantum gravity it clears up. It is often said QM can't be reconciled with GR. That's wrong. Its fits perfectly;y well into QM up to about the plank scale. Beyond that we just don't know - but that is different to what is usually said.

Thanks
Bill

 

[Prof_ Sun]

No.

Its just there is a bit of confusion about quantum gravity it clears up. It is often said QM can't be reconciled with GR. That's wrong. Its fits perfectly;y well into QM up to about the plank scale. Beyond that we just don't know - but that is different to what is usually said.

Thanks
Bill

Dear Bill,

thanks. I agree with your opinion. Your understanding on the problem is really in-depth. Do you mean that Quantum gravity is about the science up to the Planck scale? Beyond the Planck scale, of course, there is no any suitable theory up to today. Can we guess that, beyond the Planck scale, there was no time and space instead of energy or even nothing exist? Everything came from nothing, so we have $d(dG)=0$.

 

[bhobba]

Can we guess that, beyond the Planck scale, there was no time and space instead of energy or even nothing exist?.

Yes and we have guesses beyond the plank scale eg string theory.

Everything came from nothing, so we have $d(dG)=0$.

No. It came from things like the false vacuum which most definitely is not nothing. A lot of populations making such claims is sensationalist rot. Come here for the real dead. But it won't be from me because I am not an expert in this area.

Thanks
Nill

 

[enorbet]

Certainly one experiment/observation does not a proof make but it is my understanding that the ESA Integral data from 2004 re; GRB 041219A is at least hard evidence that the Universe is not grainy down to 10^ -48 meters, substantially lower than the Planck Scale by orders of magnitude. It seems to me this presents serious obstacles to String and QG theorists. True, it can't yet be said that we "know" below Planck Scale but we are not without evidence that must be addressed in any serious hypothesis.
Reference - http://www.esa.int/Our_Activities/Space_Science/Integral_challenges_physics_beyond_Einstein