I dont see a cardinality though in the grains of sand. Unless the set of all grains of sand (green and blue) has a higher cardinality than the set of green grains? — Punshhh

The set of all grains of sand, whatever colour is finite. The total number of particles in the visible universe is only 10^80!

You appeared to be discussing infinite sets earlier, which behave differently from finite sets.

I think this is as far as I can go in abstract mathematics, my interest is more in the direction of maths in the real world or where it is to be found, or relevant in/to existence. — Punshhh

If you are interested in reality, you haven't even begun to scratch the surface. Reality takes place in the continuum, where denumerable infinity is not big enough.

Yes, but numbers are ideas, so susceptible to human frailty. An alien, or a monkey, can count the grains of sand and can only come to the same conclusion, because they are not ideas. — Punshhh

Even better, get your sand and set the monkeys to work!

Let's say there is an infinite amount of grains of green sand and there is also an infinite amount of grains of blue sand, both exist. We know that if we theoretically count them as one group infinity + infinity and that we will then have an infinite amount of grains of sand, which we know are green and blue, but which are still seperate, because we are only imagining them as grouped together. Now let's imagine we mix them up so that they are all randomly mixed in together, a set of an infinite amount of grains of sand, of undefined colours. Now we could theoretically sort through this set and put all the green ones in one place and all the blue in another until we are back were we started. So we have subtracted an infinite quantity from an infinite quantity. — Punshhh

I think that's a really good idea. Why not actually perform the experiment to prove your point? Once you have demonstrated it, mathematicians will have no place to hide, they will have to accept your proof!

If you can't find two literally infinite piles of sand of different colours, why not use the odd and even numbers instead?

According to the Wikipedia article above: — Wayfarer

This paper, for example, is about t=0 and it has 487 citations!

http://journals.aps.org/prd/abstract/10.1103/PhysRevD.27.2848

Oddly enough perhaps, if we consider a world comprised of just 1 thing (whatever that may be, and assuming that makes any sense), then only "0" and "1" exist in such a world. — jorndoe

That is a (trivial) example of the mathematician's fallacy. Even in a reality that is only "comprised" of "0"s and "1"s, what exists in such a world and how it behaves, is determined by the laws of physics alone.

General relativity didn't predict the big bang, that idea was first developed by Georges Lemaître in a paper called 'The primeval atom'. — Wayfarer

"The Cosmic Atom" was an essay published in 1957.

But nevertheless, it was George leMaitre who first introduced the concept of the Big Bang, it wasn't introduced by Einstein. According to Wikipedia, the gap between LeMaitre's original paper, and the paper that introduced the Big Bang theory was actually 3 years (1927 and 1930), not thirty. (It's also interesting that Einstein is said to have exclaimed after one of LeMaitre's presentations that '"This is the most beautiful and satisfactory explanation of creation to which I have ever listened', although the provenance of the quote is contested.) — Wayfarer

1927 is 30 years prior to 1957.

I don't recall anyone claiming that Einstein developed all the solutions to his field equations and that others such as Friedmann, Lemaître, Robertson, Walker, De Sitter or Gödel weren't allowed to.

What I said was that it is impossible to 'wind the clock back' to the singularity, because at that point, there were no actual laws, nor time and space. That, I believe, is a fact. — Wayfarer

So, if general relativity is a fact, inflation is a fact, quantum mechanics is not a fact, then you are certain of the facts that obtain at the end of past-directed timelike geodesic? Good for you!

General relativity didn't predict the big bang, that idea was first developed by Georges Lemaître in a paper called 'The primeval atom'. When it was first floated, Einstein and many others resisted the idea. — Wayfarer

Your misrepresentation of the history of quantum mechanics is utterly woeful. So much so that it is difficult to summon the enthusiasm to correct you.

Fortunately in your misrepresentation of the early history of the theory of the big-bang you make the matter easy. Georges Lemaître's essay 'The primeval atom' was written 30 years after the paper in which he introduced the idea of the big-bang. The first six words of the English translation of that paper are:

According to the theory of relativity

The discovery of the big-bang is a direct consequence of general relativity, as are black-holes, wormholes, gravitational waves.

While we are on the subject, the irony is not lost on me that it is General Relativity that tells us that there has to be a "beginning", and that you prefer to pretend that there is some arbitrary barrier to science discovering *why* and *how* that event occurred.

Science doesn't 'describe reality', it describes phenomena and their causes — Wayfarer

OK, taking you at your word, what phenomena and their "causes" does quantum mechanics describe? How did we discover quantum entanglement, superposition, and even the Higgs boson, years before the phenomena were observed?

General relativity told us theoretically that there was a big-bang, and that there should be a remnant of that visible in a microwave background. General relativity told us of the existence of the perihelion effect of Mercury, time dilation necessary for GPS, black holes, and gravitational waves.

The point I'm making simply is that science doesn't explain scientific law — Wayfarer

New theories not only provide better explanations of reality, they explain why previous theories were successful or otherwise. Newton's gravity explained elliptical orbits, general relativity explained gravity in terms of curved geodesics in space-time. What makes you think this process must stop?

And there just happen to exist scientific research programs into the nature of scientific laws e.g. Constructor Theory.

So if you're looking for a 'first cause' in the sense postulated by what science means by 'cause', then you're never going to find one, because to find a cause, in the scientific sense, means that the causal relations of which 'a law' is an instance, already exist. — Wayfarer

Did the law of evolution already exist at the big bang? You keep claiming that science means something by "cause" despite the notion of "cause" being absent from our fundamental theories. Nevertheless, you don't explain why science cannot address any particular type of "cause" if it exists.

Anyway, under our fundamental time-reversible theories, it is a anthropomorphic prejudice to claim the past causes the future and not the reverse.

n the scientific sense, means that the causal relations of which 'a law' is an instance, already exist. That is why, as I understand it, physics can 'rewind the tape' of the Big Bang to within an infinitesmal of the singularity, but never to it - even in principle. — Wayfarer

No such in-principle barrier exists.

Right! That is related to the point at issue. Science (or natural philosophy) assumes 'lawful regularity' as the basis of its explanations. Discovering those regularities and making predictions on that basis, is a very large part of what science does. But science doesn't explain those regularities, although it might speculate about their origin - which is what we're doing here. So the kind of cause that science is concerned with is a cause in terms of combinations of factors and antecedents - what are called in Aristotelean terms 'efficient causes'. Whereas this kind of question concerns formal causes, which I don't think has a counterpart in much scientific thinking. — Wayfarer

That is a common (mis)conception about the nature of science, but there is another conception - the conception developed by Karl Popper, which I prefer.

According to Popper, there is no *assumption* of lawful regularity, he did, after all, dispense with induction entirely. Science, in particular our fundamental theories, are explanatory i.e. scientific theories are conjectured explanations of some aspect of the physical world that is testable.

Science as it stands explains a great number of observed regularities and irregularities. As for events such as the big bang, I'm not sure whether you would describe that as a regularity, but there are existing explanatory theories that take us back to almost the beginning of the universe, which are testable.

It doesn't seem sensible to impose arbitrary limits on what aspects of reality science can address.

Not true, because causation 'as we know it', if scientific causation is the yardstick, which it appears to be, based on your definition, this doesn't recognize formal and final causes. What, for example, causes the laws of motion to have the values they do, and not have some other values, is not a scientific question. — Wayfarer

What is "scientific causation"? When you look at the fundamental laws of nature (the ones whose constants you claim we can't inquire about scientifically) there is no mention of "cause".

Rather, it seems that "cause" in abstraction we invent in order to describe events in terms of a fundamental misconception about the nature of time -i.e. contra what our best theories tell us.

Actually initial conditions of the past cannot be determined with any current models. — m-theory

So, why did scientists look for the CMB?

And I refer you again to Hanson's experiments from last year which demonstrate, according to his testimony, non-locality.

Also, there's this: Non-locality in Quantum Field Theory due to General Relativity

The simple fact is that, contrary to your claim, experiments have supported nonlocality and sane physicists do reject locality. — Michael

Non-locality at the Planck scale? Are you for real?

What about Anton Zeilinger's 2010 experiment? — Michael

Those are experimental loopholes to ensure that Axiom 3. is maintained. You can't claim that locality is being tested if there are conceivable ways in which different parts of the experiment might influence each other.

But again, if you give it a moment's thought, do you really think Zeilinger thinks he was unable to set up his apparatus as he wished? Did he close *that* loophole?

In fact Zeilinger is on record as stating his belief in free will.

He's right that MW is local, but he's wrong about the rest, so I think my point stands. — Michael

OK, let's take the Copenhagen Interpretation and Quantum Field Theory in turn. We can then move onto String theory if you like.

The CI is a local anti-realist theory. Due to it's purely epistemic nature, it survives any experiment that refutes both local realism and non-local realism.

For example this famous experiment refutes non-local realism:
http://www.nature.com/nature/journal/v446/n7138/full/nature05677.html

You could ask yourself what it means for an epistemic theory to be non-local? The wavefunction, including the combined wavefunction of entangled particles, is not an element of reality. What does it add to say that something that does not exist here, also does not exist over there? CI is able to maintain the desirable features of locality and respecting special relativity by abandoning realism.

Hanson's experiment rules out local hidden variable theories but not local realism. — Andrew M

Feels a bit like going round in circles, but no experiment ever performed closes the "freedom loophole", so single-world realist theories that are absolutely deterministic are not ruled out by this or any other Bell-type experiment.

In particular, it doesn't rule out Many-Worlds since Many-Worlds doesn't involve any action or communication between entangled particles. — Andrew M

Yes! Many worlds is a local realist theory that cannot be ruled out by any Bell-type experiment, because of the fifth axiom which I omitted:

5. The uniqueness of outcomes.

Which is not true under Many-Worlds.

I don't know how, but that's that the scientist in charge said it did. — Michael

That's why I gave the axioms I listed earlier their proper name - axioms! Unfortunately the term "loophole" is used in two ways - to refer to the axioms themselves and to refer to the experimental difficulties.

The importance of the experiment you refer to, is that it closed two loopholes - i.e. two experimental difficulties were overcome. They were able to guarantee no-faster-than-light-communication (i.e. they closed the locality loophole) and they closed the "detection loophole", which is an experimental loophole relating to photons.

The experiment does not "support quantum nonlocality".

What about last year's loophole-free Bell test that apparently supports quantum nonlocality? — Michael

Does it really? How?

Yes it is confusing because Bell's theorem isn't a theory but rather a statement of incompatibility between a set of assumptions. Physicists who endorse the empirical and theoretical validity of QM seldom endorse assumptions (3) and (4) in Tom's table. — Pierre-Normand

Quantum field theory is explicitly local. Copenhagen is local. Many Worlds is local. As a matter of fact it has been proved that QM is a local theory. No sane physicist gives up (3)(or 2)!

One positive aspect of super-determinism is that it brings QM into compatibility with General Relativity.

So I'm right to be confused with the claim that these are axioms of the theory? — Michael

There is a contradiction produced by accepting the 4 axioms. The solutions are:

1 Axiom 4 is wrong, leading to Copenhagen or Many Worlds.

2. Axiom 3 is wrong, leading to bizarre non-local contrivances.

3. Axiom 2 is wrong, leading to Transactional interpretation??????

4. Axiom 1 and 4 are wrong, leading to Superdeterminism or Many Worlds

As I have pointed out more than once, the free will axiom is implicit in all of science, and is made explicit in quantum mechanics, particularly Bell's theorem and the various other no-go theorems. It is just as much an axiom of QM as are states in (projective) Hilbert Space.

The simple fact is that of the four axioms of Bell's theorem that I gave, the first two are regarded as unquestionable by the majority of physicists, therefore it can *only* be the last two that provide the contradiction.

There are notable exceptions to this view. Gerard 't Hooft (if you don't know him, he is a Nobel Prize winning physicist, father of the Standard Model, and of the same stature as Hawking) takes the view that freedom and counterfactual definiteness are wrong. Here's a book he wrote on the subject:

https://arxiv.org/pdf/1405.1548v3.pdf

A more accessible blog on the matter is by Sabine Hossenfelder.

http://backreaction.blogspot.co.uk/2016/01/free-will-is-dead-lets-bury-it.html

Now, counterfactual definiteness can be a surprisingly slippery notion. My view is that when it is expressed in terms of possible measurements, then that statement is incompatible with the absence of free will.

So, what Bell's theorem purports to show is that local counterfactual definiteness is forbidden by quantum mechanics, while the axioms of freedom and causality are protected.

There is of course another way of rendering Bell's theorem impotent - the Everett Interpretation.

Bell's theorem just is the statement that the statistical predictions of QM are inconsistent with all local hidden variable theories. — Pierre-Normand

Since you refuse to provide the axioms of Bell's theorem, allow me:

1. Freedom of choice. The freedom to choose which experiment to perform independently of the object to be measured. i.e. The Free Will of the Experimenter

2. Measurement Independence. Future outcomes do not influence past settings - i.e. causality.

3. Locality.

4. Counterfactual Definiteness.

Doe it take time to experience, or can you experience in the absence of time? If so, i.e. if time is an unnecessary component of experience, then how is that possible?

Intuitively, space is the nearest physical concept I have. — bert1

What about time?

You state that as a fact which it is not. The weight of modern scholarship is very much against you on this point. — Barry Etheridge

Is there a contemporary account of Jesus?

From my panpsychist point of view it is reality-as-continuum (as opposed to reality as plurality of discrete bits) that is the experiencer. — bert1

What does "reality-as-contunuum" mean?

You are misunderstanding Bell's statement. Bell's theorem is derived from the assumption of local hidden variables — Pierre-Normand

What are the axioms of Bell's Theorem?

I have never heard of any axiom of free will in quantum mechanics. — m-theory

In Bell's ow words:

There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the “decision” by the experimenter to carry out one set of measurements rather than another, the difficulty disappears. There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already “knows” what that measurement, and its outcome, will be.

Often the Free Will Axiom is called the "free will loophole", or the "free choice of detector orientations".

I think it is important to point out that no classical or modern theory gives us a good account of initial conditions of the past.
Not GR or the standard model.
If they did, then sure you could claim they were deterministic. — m-theory

I think you are missing the point. Given the conditions now, the past can be calculated by physical laws. This is how we know the big bang happened. Both General Relativity and the Standard Model have time reversal operators.

But GR and the standard model do not predict the past initial conditions, we still cannot claim to know nor do we have a complete account of the initial conditions. — m-theory

Umm, so why did we ever look for CMB?

I didn't say I don't know what it it is, I'm just not interested in arguing about what it is.

Anyway, despite the accusations to the contrary, I have already explained why the photon cannot experience anything. I have also stated that this explanation does not extend to particles with mass. Thus panpsychism can be recovered if you are that desperate.

However, I am curious about the implications of indistinguishability on the assumption that massive particles possess consciousness.

Then it should be very easy for you to write a valid deduction that demonstrates that. Yet despite repeated requests, you have not done that.

I assume you are aware that 'Well then show me how P could be true!' is not a deduction of not-P. If it were, Goldbach's conjecture and most other unsolved conjectures of mathematics would be solved. — andrewk

You define what a mental state is, and I'll show you why the photon cannot possess it. Deal?

All of them. Relativity deserves special mention though, as I have repeatedly mentioned.

There's me hoping that you were going to argue that particles must be emotional because the Free Will theorem did not claim they were *not* emotional and that an extra premise was needed.

I'm glad however, that you agree that relativistic particles - i.e. entities that cannot experience anything including the passage of time - cannot possess mental states.

So, according to the laws of physics, photons cannot possess consciousness, though they (if humans do) may possess a modicum of freedom.

But of course, panpsychism could only apply to matter particles...

What do you think photons are conscious of?

If relativistic spin 1 particles possess freedom, then consciousness is not required for freedom. It is that simple.

Now, what do you think photons are conscious of?

What do you think a relativistic spin 1 particle might be conscious of?

You don't need to assume a relativistic spin 1 particle does not possess consciousness.

If particles possess freedom, then consciousness is not required, or even possible in that case.

Well, if we accept the free will theorem, and if free will requires consciousness, then it seems that panpsychism is consistent with the laws of physics. — Michael

You mean despite the fact that the Free Will Theorem demonstrates that free will does not require consciousness?

But anyways, it does seem like a logical conclusion once you acknowledge that qualia simply has to be fundamental and cannot be an emergent phenomenon. — Weeknd

Why do qualia have to be "fundamental", particularly as the human brain is the only object in the universe known to possess them?

Your claim that qualia cannot be emergent does not seem to tally with the observation that they can be affected by tampering with the physical substrate from which they emerge.

Except that is exactly what happens in one of the most famous optical illusions. We simply do not see an exact map of the photons received at the retina. — Barry Etheridge

We certainly don't! This is my favourite optical illusion: