I Latest Gamma Ray Burst Experimental results

[Azurite]

with regards to this https://arxiv.org/abs/1103.5626
"Gamma ray burst delay times probe the geometry of momentum space"

May we have updates of the latest experiment results along the line of Smolin 2011 idea concerning gamma ray burst delay times that can test if momentum space is curved?

 

[PAllen]

with regards to this https://arxiv.org/abs/1103.5626
"Gamma ray burst delay times probe the geometry of momentum space"

May we have updates of the latest experiment results along the line of Smolin 2011 idea concerning gamma ray burst delay times that can test if momentum space is curved?

The binary neutron star merger, observed via GW, many frequencies of EM, and gamma rays, puts extremely stringent bounds on any such phenomenon. For all practical purposes it rules it out. All the waves arrived at the same time to better than one part in 10¹⁵.
https://arxiv.org/abs/1710.05834

 

[Azurite]

The binary neutron star merger, observed via GW, many frequencies of EM, and gamma rays, puts extremely stringent bounds on any such phenomenon. For all practical purposes it rules it out. All the waves arrived at the same time to better than one part in 10¹⁵.
https://arxiv.org/abs/1710.05834

So did this test categorically constrain or refute Lee Smolin conjecture that momentum space could be curved (or relative locality)?

But then.. did the test also rule out we could be living in Phase space? (where spacetime and momentum space are not fundamental). Does this idea require momentum space to be curved or relative locality? or no connection? Please see:

https://www.newscientist.com/article/mg21128241-700-beyond-space-time-welcome-to-phase-space/

 

[PeterDonis]

So did this test categorically constrain or refute

Science doesn't work that way. You can't "categorically refute" a hypothesis because there are always finite error bars in our measurements. But you can evaluate the likelihood of a hypothesis based on the data.

did the test also rule out we could be living in Phase space?

You'll need to give an actual peer-reviewed paper that makes testable predictions based on this hypothesis. A New Scientist article is not enough. (New Scientist is notorious for reading way too much into relatively innocuous experimental results.)

 

[mfb]

But you can evaluate the likelihood of a hypothesis based on the data.

Not in a strict mathematical sense. You can only evaluate the likelihood of the data based on a hypothesis. If that is small enough, then at some point you drop the hypothesis.

 

[PeterDonis]

Not in a strict mathematical sense. You can only evaluate the likelihood of the data based on a hypothesis.

A better way to put what I was trying to say is that, in Bayesian terms, given a set of data, you can evaluate the likelihood ratio for any hypothesis based on that set of data. That in itself is not sufficient to give you the likelihood of the hypothesis, because you also need a prior for that.

 

[Azurite]

The binary neutron star merger, observed via GW, many frequencies of EM, and gamma rays, puts extremely stringent bounds on any such phenomenon. For all practical purposes it rules it out. All the waves arrived at the same time to better than one part in 10¹⁵.
https://arxiv.org/abs/1710.05834

Can someone else like perhaps mfb confirms whether this latest experiment has indeed rules out momentum space can be curved? What loopholes or arguments that says Smolin original argument is not valid that the gamma ray burst delay times tests have nothing to do momentum space being curved?

 

[PAllen]

Can someone else like perhaps mfb confirms whether this latest experiment has indeed rules out momentum space can be curved? What loopholes or arguments that says Smolin original argument is not valid that the gamma ray burst delay times tests have nothing to do momentum space being curved?

The older tests are more ambiguous and less precise, and never accepted as having the meaning implied by the New Scientist article. The neutron star merger is a clean test of extremely high precision. The key to the neutron star merger is that we know the signal generation is simultaneous, and the distance is large. This leads to a clean, high precision test, showing that ther is no delay (to extremely high precision). Any theory that predicts a delay is thus falsified.

 

[Azurite]

The older tests are more ambiguous and less precise, and never accepted as having the meaning implied by the New Scientist article. The neutron star merger is a clean test of extremely high precision. The key to the neutron star merger is that we know the signal generation is simultaneous, and the distance is large. This leads to a clean, high precision test, showing that ther is no delay (to extremely high precision). Any theory that predicts a delay is thus falsified.

Is it not loop quantum gravity has similar gamma ray burst delay times prediction or have they modified LQG so it won't satisty it anymore. I wonder if the "momentum space can be curved" folks have do similar modifications (?)

 

[Azurite]

So did this test categorically constrain or refute Lee Smolin conjecture that momentum space could be curved (or relative locality)?

But then.. did the test also rule out we could be living in Phase space? (where spacetime and momentum space are not fundamental). Does this idea require momentum space to be curved or relative locality? or no connection? Please see:

https://www.newscientist.com/article/mg21128241-700-beyond-space-time-welcome-to-phase-space/

I'm still a bit confused by Smolin referring to momentum space as possibly real. As we know. Momentum space is just plots of the energy and momentum of the particle. What is the difference if the momentum space is real and not real? If real.. does it mean somewhere there is a momentum space where energy and momentum is there.. or does it mean energy and momentum of a particle is real.. but then we know energy and momentum is real.. so can anyone explain at least what Lee Smolin meant by momentum space being real versus not real?

 

[Mentz114]

I'm still a bit confused by Smolin referring to momentum space as possibly real. As we know. Momentum space is just plots of the energy and momentum of the particle. What is the difference if the momentum space is real and not real? If real.. does it mean somewhere there is a momentum space where energy and momentum is there.. or does it mean energy and momentum of a particle is real.. but then we know energy and momentum is real.. so can anyone explain at least what Lee Smolin meant by momentum space being real versus not real?

Are you familiar with the concept of a space-time defined by a metric tensor ? Smolin was proposing entirely new physics when he came up with the idea that we can define a new 'space-time' not by using a metric that defines spatial intervals (GTR is such a theory), but one which uses momentum instead of position. He thought that dynamics could then be rewritten in simpler terms in this 'space-time' ( which could possesses intrinsic curvature).

I think you may be confusing the wave-function in the momentum basis with Smolins abstract space.

 

[Azurite]

Are you familiar with the concept of a space-time defined by a metric tensor ? Smolin was proposing entirely new physics when he came up with the idea that we can define a new 'space-time' not by using a metric that defines spatial intervals (GTR is such a theory), but one which uses momentum instead of position. He thought that dynamics could then be rewritten in simpler terms in this 'space-time' ( which could possesses intrinsic curvature).

I think you may be confusing the wave-function in the momentum basis with Smolins abstract space.

I know what Smolin meant by his new objective momentum space but what I still can't get is that supposed for sake of discussion.. you are living in pure momentum space (let's say spacetime that uses the position metric didn't exist). What would happen to you in the momentum space? Does it mean you would be pure waves only, but would you still have a particle? or does momentum space mean there is no particle but just waves (I'm saying no particle since spacetime that uses position didn't exist.. for sake of discussion).

 

[Mentz114]

I know what Smolin meant by his new objective momentum space but what I still can't get is that supposed for sake of discussion.. you are living in pure momentum space (let's say spacetime that uses the position metric didn't exist). What would happen to you in the momentum space? Does it mean you would be pure waves only, but would you still have a particle? or does momentum space mean there is no particle but just waves (I'm saying no particle since spacetime that uses position didn't exist.. for sake of discussion).

Those questions seem to be like asking if we would feel the Earths gravity if Newton had not formulated his gravitational theory.

Theories are like descriptions or models of phenomena - they are not the phemonema themselves.

 

[Azurite]

Those questions seem to be like asking if we would feel the Earths gravity if Newton had not formulated his gravitational theory.

Theories are like descriptions or models of phenomena - they are not the phemonema themselves.

I just want to have idea of what's it's like to be living in pure momentum space. Remember in pure MWI, there is only the unitary state vector and no preferred basis. What if instead of position, it's momentum that is the object of some bohmian basis. What would happen to you living in a universe that has only momentum space as the metric (not position)? just hope you can answer this as I've been thinking of this for over a week.

 

[PeterDonis]

I just want to have idea of what's it's like to be living in pure momentum space.

I don't think there is any such thing, and I don't think this is what Smolin was proposing (although without a reference to an actual paper of Smolin's describing his model I can't be sure). "Momentum space" and "position space" are not two separate things; they are two different ways of looking at the same thing.

 

[Mentz114]

I just want to have idea of what's it's like to be living in pure momentum space. Remember in pure MWI, there is only the unitary state vector and no preferred basis. What if instead of position, it's momentum that is the object of some bohmian basis. What would happen to you living in a universe that has only momentum space as the metric (not position)? just hope you can answer this as I've been thinking of this for over a week.

When Smolin did this work he was not trying to invent a new universe, he was trying to describe/model the only one we know. If the calculations predict that everything will be the same then he would count that as a success. If his theory predicts that water will flow up hills - the theory is describing some exotic thing and is not a success.

I know next to nothing about this work so you have to study it and look for the answer there.

 

[PAllen]

And if it predicts that high energy gamma rays are delayed compared to lower frequency EM over long distances, then it is falsified

 

[Azurite]

I don't think there is any such thing, and I don't think this is what Smolin was proposing (although without a reference to an actual paper of Smolin's describing his model I can't be sure). "Momentum space" and "position space" are not two separate things; they are two different ways of looking at the same thing.

The Smolin paper is https://arxiv.org/PS_cache/arxiv/pdf/1101/1101.0931v2.pdf (this paper was listed in the article above)

I guess it is not possible to have momentum and energy axis only because you need time for there to be dynamic.

In our present world. We have spacetime in position basis or metric. But supposed, just for sake of discussion and understanding.. supposed we could create a new big bang and we are free to choose what spacetime metric to program. Supposed we only choose 1/length on one axis and 1/time in another axis.. remember:

The inverse of distance is number per unit distance which is a spatial frequency.
The inverse of time is number per unit time which is a temporal frequency.

Supposed there were a universe with only spatial frequency and temporal frequency.. would this universe have objects or wave only?

 

[PeterDonis]

we are free to choose what spacetime metric to program. Supposed we only choose 1/length on one axis and 1/time in another axis

This isn't what "choosing a spacetime metric" means. A spacetime metric has units of length/time. It doesn't have units of 1/length or 1/time. If you have a thingy with units of 1/length and 1/time, it isn't a spacetime metric.

Supposed there were a universe with only spatial frequency and temporal frequency

There is no such thing. If you have 1/length and 1/time, then you have length and time; you just take the reciprocals of your units. There's no way to not allow that if you're using math.

 

[Azurite]

This isn't what "choosing a spacetime metric" means. A spacetime metric has units of length/time. It doesn't have units of 1/length or 1/time. If you have a thingy with units of 1/length and 1/time, it isn't a spacetime metric.
There is no such thing. If you have 1/length and 1/time, then you have length and time; you just take the reciprocals of your units. There's no way to not allow that if you're using math.

If you have a particle described by distance and time.. what is the application or advantage where you have to describe it by 1/length or 1/time? Can you please give an example. Thank you.

 

[PeterDonis]

If you have a particle described by distance and time.. what is the application or advantage where you have to describe it by 1/length or 1/time?

If you are using quantum mechanics in natural units (in which $\hbar = 1$), then, heuristically, momentum is 1/length and energy is 1/time. Particle physicists switch between length/time scales and momentum/energy scales using this heuristic all the time.

 

[Azurite]

If you are using quantum mechanics in natural units (in which $\hbar = 1$), then, heuristically, momentum is 1/length and energy is 1/time. Particle physicists switch between length/time scales and momentum/energy scales using this heuristic all the time.

Can 1/length and 1/time never be separate degrees of freedom? For example. Our spacetime has length and time.. and the thing in 1/length and 1/time are just things in spacetime which are localized in the Fourier transformed description of spacetime.. however this is in contrast to this mathematic possibility that you could have a genuinely separated reciprocal space with extra degrees of freedom. Is this not even possible mathematically?

 

[PeterDonis]

Is this not even possible mathematically?

I'm not aware of any model that works like this. Certainly it's not how standard quantum field theory works.

 

[Azurite]

If you are using quantum mechanics in natural units (in which $\hbar = 1$), then, heuristically, momentum is 1/length and energy is 1/time. Particle physicists switch between length/time scales and momentum/energy scales using this heuristic all the time.

How about in classical mechanics where there is no. $\hbar = 1$, isn't momentum = 1/length and energy = 1/time anymore? why?

 

[PeterDonis]

How about in classical mechanics

In classical (non-quantum) physics, yes, you don't have "natural" units in which momentum = 1/length and energy = 1/time. The "natural" units of classical (non-quantum) relativity are $c = 1$, so momentum and energy have the same units, and length and time have the same units, but there isn't a reciprocal relation between them.

 

[Nugatory]

How about in classical mechanics where there is no. $\hbar = 1$, isn't momentum = 1/length and energy = 1/time anymore? why?

The classical formulas are $p=mv$ and $E_k=mv^2/2$. You can work out the units for yourself.

 

[Azurite]

In classical (non-quantum) physics, yes, you don't have "natural" units in which momentum = 1/length and energy = 1/time. The "natural" units of classical (non-quantum) relativity are $c = 1$, so momentum and energy have the same units, and length and time have the same units, but there isn't a reciprocal relation between them.

Is the following how it is derived.. how the reciprocal relationship comes about:

E=mc^2 = (mc) (c)
since mc is just mass times speed, the momentum p of a photon...

E= (p) (c) = (p) (f x wavelength)

using c (speed) = f(frequency) times wavelength for waves
Equating E = hf from the Planck/Einstein relation to the expression above, we obtain:

(h) (f) = (p) (f x wavelength)

giving h/p = wavelength

and p = h/wavelength

and since k (wave number) = 1/wavelength

then p = hk

however, you said momentum is 1/length... but the above shows p = h/wavelength... not length... how did wavelength become length?

 

[PeterDonis]

you said momentum is 1/length

I said the units of momentum, in natural quantum units where $\hbar = 1$, are 1/units of length.

how did wavelength become length?

If we are talking about the wave function of a quantum object, "wavelength" is the relevant quantity with units of length.

 

[Azurite]

Are you familiar with the concept of a space-time defined by a metric tensor ? Smolin was proposing entirely new physics when he came up with the idea that we can define a new 'space-time' not by using a metric that defines spatial intervals (GTR is such a theory), but one which uses momentum instead of position. He thought that dynamics could then be rewritten in simpler terms in this 'space-time' ( which could possesses intrinsic curvature).

I think you may be confusing the wave-function in the momentum basis with Smolins abstract space.

Was Smolin attempt shows we can't even tell if we have spacetime defined with a metric that defines spatial intervals or one which uses momentum??

What are possible observables (what's the right term for this?) you can use as metric in spacetime besides, spatial, temporal, momentum and energy where you can't distinguish which is which? how about spin?

 

[PeterDonis]

Was Smolin attempt shows we can't even tell if we have spacetime defined with a metric that defines spatial intervals or one which uses momentum??

Please stop posting references from New Scientist. It is not a valid source, and you should not be trying to learn physics from it.

Smolin's hypothetical proposal is very advanced, and it's also very speculative. Any thread discussing it should really be at the "A" level, and it's not really clear how much of a useful discussion we can have about it here anyway, since it's speculative. But any discussion needs to be based on actual quotes from his actual paper, not on diagrams from New Scientist.

 

[Azurite]

This isn't what "choosing a spacetime metric" means. A spacetime metric has units of length/time. It doesn't have units of 1/length or 1/time. If you have a thingy with units of 1/length and 1/time, it isn't a spacetime metric.
There is no such thing. If you have 1/length and 1/time, then you have length and time; you just take the reciprocals of your units. There's no way to not allow that if you're using math.

you said spacetime metric can't be 1/length or 1/time.. so if particle physicists use graph of them, then what they are called and how do you differentiate from spacetime diagram?

 

[PeterDonis]

if particle physicists use graph of them

Where did I say anything about a "graph"? I said particle physicists routinely switch between space/time units and momentum/energy units, which in quantum field theory with $\hbar = 1$ are reciprocals of each other.

Particle physicists use Feynman diagrams, which are most often drawn using momentum/energy, but I don't know if I would call those a "graph" in the sense you mean, since they're highly schematic and don't represent particles having any particular momentum or energy, but represent terms in integrals over a whole range of momenta and energies.

 

[Azurite]

Where did I say anything about a "graph"? I said particle physicists routinely switch between space/time units and momentum/energy units, which in quantum field theory with $\hbar = 1$ are reciprocals of each other.

Particle physicists use Feynman diagrams, which are most often drawn using momentum/energy, but I don't know if I would call those a "graph" in the sense you mean, since they're highly schematic and don't represent particles having any particular momentum or energy, but represent terms in integrals over a whole range of momenta and energies.

Ok thanks.
From a historical perspective. Einstein created spacetime with spatial metric concept even without quantum mechanics... this means even if quantum mechanics didn't exist.. spacetime is still valid.. so at that time Einstein never try to think about momentum space with momentum metric and this is just latter conjecture after qm and Planck h.. right?

So if momentum space metric is related to quantum mechanics.. this means spacetime with spatial metric is still more fundamental since one can propose this without quantum mechanics?

 

[PeterDonis]

even if quantum mechanics didn't exist.. spacetime is still valid

Yes.

at that time Einstein never try to think about momentum space with momentum metric

The concept of "momentum space", in terms of using momentum-energy units instead of space-time units, does not require quantum mechanics. Einstein did not look at things this way as far as I know, but then again he didn't initially pick up the spacetime concept either when Minkowski published it in 1907. It wasn't until Einstein realized that spacetime geometry was the concept he needed for a relativistic theory of gravity that he started thinking in terms of spacetime.

if momentum space metric is related to quantum mechanics

It isn't. See above. QM uses it, but that doesn't mean it's only valid in QM.

 

[Azurite]

Yes.
The concept of "momentum space", in terms of using momentum-energy units instead of space-time units, does not require quantum mechanics. Einstein did not look at things this way as far as I know, but then again he didn't initially pick up the spacetime concept either when Minkowski published it in 1907. It wasn't until Einstein realized that spacetime geometry was the concept he needed for a relativistic theory of gravity that he started thinking in terms of spacetime.
It isn't. See above. QM uses it, but that doesn't mean it's only valid in QM.

Also note spacetime metric doesn't hold in non-relativistic quantum mechanics in the schrodinger equation. Therefore using 1/length and 1/space doesn't mean it's using spacetime metric... so for purposes of illustration is it not incorrect to use 1/length and 1/space graphs for depicting momentum and energy in non-relativistic QM? Does anyone make such graph? I'm not talking about relativistic qft Feynman diagram but non-relativistic QM.

 

[PeterDonis]

spacetime metric doesn't hold in non-relativistic quantum mechanics in the schrodinger equation

Well, of course, since there is no "spacetime metric" in non-relativistic physics.

Therefore using 1/length and 1/space doesn't mean it's using spacetime metric

In non-relativistic physics, that's correct, you can adopt "natural" quantum units without using a spacetime metric.

so for purposes of illustration is it not incorrect to use 1/length and 1/space graphs for depicting momentum and energy in non-relativistic QM?

What would "1/length and 1/space graphs" look like?

Does anyone make such graph?

I don't know, since I don't know what you mean by those terms.

 

[Azurite]

Well, of course, since there is no "spacetime metric" in non-relativistic physics.
In non-relativistic physics, that's correct, you can adopt "natural" quantum units without using a spacetime metric.
What would "1/length and 1/space graphs" look like?
I don't know, since I don't know what you mean by those terms.

Reference frames can be anything from basic 4 dimensional Einstein spacetime to the 6 compactified dimensions in superstring theory, etc.. How about non-relativistic reference frames.. is Galilean space also a reference frame? What are other non-relativistic reference frames?

 

[PeterDonis]

Reference frames

The things you are describing are not reference frames. They are manifolds.

 

[Azurite]

The things you are describing are not reference frames. They are manifolds.

Space, reciprocal space are reference frames.
Spacetime, calabi-yau compactified dimensions are manifolds.

Right?

So "reference frames" are used for non-relativistic space? So Galilean space is a reference frame and not manifold. Right?

 

[Azurite]

Space, reciprocal space are reference frames.
Spacetime, calabi-yau compactified dimensions are manifolds.

Right?

So "reference frames" are used for non-relativistic space? So Galilean space is a reference frame and not manifold. Right?

I found out there are many meaning of reference frames:

https://en.wikipedia.org/wiki/Frame_of_reference

"The need to distinguish between the various meanings of "frame of reference" has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in Cartesian frame of reference. Sometimes the state of motion is emphasized, as in rotating frame of reference. Sometimes the way it transforms to frames considered as related is emphasized as in Galilean frame of reference. Sometimes frames are distinguished by the scale of their observations, as in macroscopic and microscopic frames of reference.[1]"

I want to ask about reference frames as used in Newtonian space or non-relativistic quantum mechanics..

Does it make sense or semantically correct to say the reference frame of particles are direct space (x,y,z,t).. while the reference frame of waves are reciprocal space (with axis kx, ky, kz, kt)? Any instructor teach in this manner (to undergraduate for instance) or it is ok for laymen?

 

[PeterDonis]

Space, reciprocal space are reference frames.
Spacetime, calabi-yau compactified dimensions are manifolds.

Right?

No. "Space" is a manifold. I don't know what you mean by "reciprocal space".

So "reference frames" are used for non-relativistic space? So Galilean space is a reference frame and not manifold. Right?

Wrong. "Galilean space" is a manifold.

I found out there are many meaning of reference frames

Yes, but none of them correspond to the way you are using the term.

I want to ask about reference frames as used in Newtonian space or non-relativistic quantum mechanics

Then you should just ask, instead of making claims that are wrong and then asking if they are right.

Does it make sense or semantically correct to say the reference frame of particles are direct space (x,y,z,t).. while the reference frame of waves are reciprocal space (with axis kx, ky, kz, kt)?

No.

 

[Azurite]

No. "Space" is a manifold. I don't know what you mean by "reciprocal space".
Wrong. "Galilean space" is a manifold.
Yes, but none of them correspond to the way you are using the term.
Then you should just ask, instead of making claims that are wrong and then asking if they are right.
No.

When one creates a universe with spacetime. It automatically has momentum because there is a position, right?

But should it automatically produce the quantum configuration space or is this an additional thing?

If it is an additional thing. What kind of manifold can house the quantum configuration space.. so maybe one adds 2 manifolds together.. the spacetime manifold and the extra quantum configuration space manifold?

 

[PeterDonis]

When one creates a universe with spacetime. It automatically has momentum because there is a position, right?

I don't know what you mean by this.

should it automatically produce the quantum configuration space or is this an additional thing?

I don't know what you mean by this either.

As I said before, you seem to me to be speculating without a good conceptual basis.

 

[Azurite]

I don't know what you mean by this.

I just meant whenever there was a universe with spacetime.. it should automatically have position and momentum. Correct?

But should it also somehow contain the quantum configuration space? Or is this extra?

I don't know what you mean by this either.

As I said before, you seem to me to be speculating without a good conceptual basis.

 

[PeterDonis]

I just meant when there was a universe with spacetime.. it should automatically have position and momentum. Correct?

Spacetime doesn't have position and momentum. Particular objects in spacetime have position and momentum.

should it also somehow contain the quantum configuration space? Or is this extra?

I still don't know what you mean. We don't create the universe, we just discover what it's like. We don't get to pick whether it has a quantum configuration space or not, or whether it's a spacetime, or whether objects have position and momentum. So your questions seem meaningless to me.

 

[Azurite]

Spacetime doesn't have position and momentum. Particular objects in spacetime have position and momentum.
I still don't know what you mean. We don't create the universe, we just discover what it's like. We don't get to pick whether it has a quantum configuration space or not, or whether it's a spacetime, or whether objects have position and momentum. So your questions seem meaningless to me.

In the string landscape or multiverse or others.. each universe has different laws of nature. I just want to differentiate or understand what it would be like to have spacetime only without configuration space.

Or I just want to understand how to relate spacetime and configuration space.

Is manifold used for configuration space? What is the relationship between manifold and configuration space?

 

[Azurite]

In the string landscape or multiverse or others.. each universe has different laws of nature. I just want to differentiate or understand what it would be like to have spacetime only without configuration space.

Or I just want to understand how to relate spacetime and configuration space.

Is manifold used for configuration space? What is the relationship between manifold and configuration space?

Configuration space is like the Hamiltonian phase space.. describing 2 particles with 6 dimensions.. and for more particles (infinite).. it is infinite dimensional...

A manifold is not a phase space but has a limit..

so I guess this is the main difference between the two. Right?

About the pilot wave.. it is vague as it is in configuration space... but can't you make the pilot wave like marbles in a box.. the marbles have multidimensional hamiltonian phase space but it doesn't mean the marbles don't exist in 3D.. likewise.. for those who propose pilot wave use some quantum force that has quanta or particles... can it occur just like the marbles? What manifold do you describe this real pilot wave? spacetime too? To distinguish. Others use the terms "Reciprocal space" but I think this is very vague terms hence mustn't be used. So what should the term/jargon for the manifold that house the real pilot waves?

 

[PeterDonis]

In the string landscape or multiverse or others.. each universe has different laws of nature.

No, each universe just has particular values for a bunch of physical constants that are free parameters in our current laws of nature. And anyway all that is speculative, there's no evidence for it. And in any case, the speculative models you mention don't look anything like what you are asking about.

I just want to differentiate or understand what it would be like to have spacetime only without configuration space.

I don't know of any such model.

I just want to understand how to relate spacetime and configuration space.

That's way too broad for a PF thread. You're asking for several undergraduate courses' worth of information.

Is manifConfiguration space is like the Hamiltonian phase spaceold used for configuration space? What is the relationship between manifold and configuration space?

Configuration space is an example of a manifold. If you want to know what a manifold is, again, you're basically asking for a course in mathematical physics. If you don't already have that background then you need to take the time to learn it. There are no shortcuts.

 

[PeterDonis]

Configuration space is like the Hamiltonian phase space

No, it isn't. Phase space contains "dimensions" for both position and momentum. Configuration space only contains "dimensions" for position.

A manifold is not a phase space but has a limit

Phase space is a manifold. I have no idea what you mean by "has a limit".

so I guess this is the main difference between the two. Right?

No. See above.

About the pilot wave

Again, this is much too broad for a PF discussion; you are basically asking for a course in QM. You need to take the time to learn it yourself.

 

[PeterDonis]

At this point I am closing the thread since no useful progress is being made. @Azurite , given your apparent lack of background in math and physics, the method you seem to be pursuing, of guessing what various terms mean and then asking if your guesses are right, is not going to work well. As I said in the last couple of posts, you need to take the time to actually work through several courses' worth of material, without trying to guess in advance what it is going to tell you. If during that process you have particular questions about particular items, you can post specific threads here about them. But you're basically trying to start from scratch and get all that several courses' worth of material from PF. That's not what PF is for (and, as noted above, the method you're using doesn't work well anyway).