Guest essay by Nancy Green
At the close of the 19th century physics was settled science. The major questions had been answered and what remained was considered window dressing. Our place in the universe was known:
We came from the past and were heading to the future. On the basis of Physical Laws, by knowing the Past one could accurately predict the Future.
This was the Clockwork Universe of the Victorian Era. We knew where we came from and where we were going. However, as often happens in science, this turned out to be an illusion.
A century before, the double-slit experiment had overturned the corpuscular theory of light. Light was instead shown to be a wave, which explained the observed interference patterns. However, Einstein’s 1905 paper on the photoelectric effect turned the wave theory of light on its head.
We now accept that Light is composed of particles (photons) that exhibit wave-like behavior. Each photon is a discrete packet of energy (quanta), determined by the frequency of the wave. What Einstein did not envision was the implications of this discovery, which led to the famous quote, “God does not play dice”.
But as it turns out, with our present level of understanding, God does play dice. Consider the dual slit light experiment. What does it tell us about the nature of our universe when we view light as particles?
In the dual slit experiment, light from point A is shone towards point B. What we find is that the individual photons will go through slit 1 or slit 2 to reach point B, but there is no way to determine at Point A which slit (path) the photons will choose. And equally perplexing, there is no way to determine at Point B which path the individual photons will arrive from. Relabeling the slits as paths we have:
This property is not confined to light; it can also be recreated with other particles. The implications are profound. Point A has more than one possible future, and Point B has more than one possible past. Rearranging our double slit experiment so that A and B coincide with the Present, we end up with:
Which we can simplify:
Our Victorian Era picture of one future and one past is no longer correct. Our deterministic view of the world now becomes probabilistic. Some futures and some pasts are more likely than others, but all are possible. Our common sense notion (theory) of one past and one future does not match reality, and when theory does not match reality, it is reality that is correct.
Now you may say, well that may be true for very small particles, but surely it doesn’t apply to the real world. Consider however, that in place of a particle, we used you the reader.
Let point A be your office and point B your home. Some days you will travel from the office to home via path 1. On other days however, maybe you need to go shopping first, or meet friends, or your car may break down, or any number of activities may require you to take path 2 to reach home. So you take path 2.
For all intents and purposes your behavior mimics the behavior of a particle. An outside observer will not be able to tell which path you are likely to take. To an outside observer your “free will” is no different than the behavior of the particle. To the observer the reason for both behaviors is “unknown” or “chance”. It cannot be determined, except as a probability.
Chaos is routinely discussed when considering models. What does our double slit experiment tell us about Chaos?
Consider that instead of starting at point A, we start at A1. A1 is a microscopic distance along the path from A to P1. Or, instead we start at point A2, which is a microscopic distance along the path from A to P2.
From geometry, A1 and A2 will be an even smaller distance from each other than they are from A. They are less than a microscopic distance from each other, yet they lead to different futures. At A1 you can only travel to P1. At A2 you can only travel to P2. Thus with a less than microscopic difference in “initial values” we get two different futures, neither of which is wrong.
But wait you say, ignoring that P1 and P2 are in A’s future, they both lead to the same future. They lead to B. But in point of fact, B is only one possible future. We purposely kept the diagram simple. Reality is more complex. From points P1 or P2 the particle may travel to a whole range of futures. (thus the interference pattern of the double slit experiment).
And this is what we see when trying to forecast the weather or the stock market. Very small differences in the values of A1 or A2 quickly lead to different futures. All the futures are possible; some are simply more likely than others. But none are wrong.
Climate Science and the IPCC argue that climate is different. Because climate is the average of weather, we should be able to average the results of weather models and arrive at a skillful prediction for future climate. However, does this match reality?
![clip_image018[1]](http://wattsupwiththat.files.wordpress.com/2014/03/clip_image0181.png?quality=75 "clip_image018[1]")
Climate science argues that future climate = (C+D+B)/3, where 3 = number of models.
However, climate is not the average over models. Climate is the average over time. Thus:
If we arrive at B via path 1, then climate = (A+P1+B)/3, where 3 = elapsed time
If we arrive at B via path 2, then climate = (A+P2+B)/3, where 3 = elapsed time
Since P1 <> P2, even though we have arrived at the identical future B, we have two different climates, none of which resemble the IPCC ensemble model mean. And this only considers future B.
Futures C and D are also possible, with different probability. We will arrive at one, but there is no way to determine in advance which one. Thus for a single starting point A, there is an infinite number of future climates that are all possible. Some are simply more likely than others.
Thus the failure of climate models to predict the future. The IPCC model mean predicts B, simply because it happens to be in the middle. However, this is simply accidental. As the “Pause” demonstrates, nature is free to choose C, B, or D, and in the real world nature has chosen D. As a result the models are diverging from reality.
In reality the models are attempting an impossible task. There are not simply 3 futures and are not simply 2 paths; there are for all intents and purposes an infinite number of futures, and an infinite number of paths. All are possible.
Some futures are more likely, but that is simply God is playing dice. We are not guaranteed to arrive at any specific future, thus there is nothing for the climate models to solve. They are being asked to deliver an impossible result and like Hal in 2001 they have gone crazy. They are killing people by cutting life support via energy poverty.
HAL: “The 9000 series is the most reliable computer ever made. No 9000 computer has ever made a mistake or distorted information. We are all, by any practical definition of the words, foolproof and incapable of error”.
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“Godel is useful for predicting why a closed system like a computer program cannot predict the future”
Computer programs predict the flights of spacecrafts. If Godel was a problem, the Apollo astronauts would be dead.
“Free will is inconsistent with determinism, because your decisions would depend on the state of the universe before you were born.”
This is physically impossible because your brain did not exist before you were born. Present state depends on previous state but not previous states 13 billion years ago.
In case the significant of hidden variables is unclear. I hold out my hands with a coin in one. Based on which hand contains the coin, I will take path 1 (left) or path 2 (right) to the future. Your task is to find out which hand contains the coin, so that you can predict which path I will take and thus predict the future.
I known the hidden variable (which hand contains the coin) so I can predict my actions deterministically, but since you don’t know the hidden variable your must predict my actions probabilistically.
Bell’s Theorem establishes that there is no hidden variable to tell us which path will be chosen to the future. Thus, our common sense belief that there is only one possible future which is determined by the present and physical laws is false. Therefore the future cannot be determined, except of the basis of probabilities.
Dolan
Don’t be offended. I don’t lecture. I would rather you do your own self-study. BTW I’m referring to Boltzmann’s formulation of the 2nd law. If you’re thinking of Clausius or Kelvin’s formulation, I see why you disagree.
I’m afraid you misunderstood Godel’s theorems. The fact that you’re saying Edward Nelson proved Peano arithmetic to be inconsistent is actually the proof that Godel’s theorems do not apply to Peano arithmetic. The theorems apply to logical systems whose completeness and/or consistency are unprovable. BTW majority of mathematicians accept Gentzen’s proof that Peano’s axioms are consistent. But that’s beside the point.
I do not dismiss relativity theory. It is correct. I merely pointed out that it’s deterministic.
This is physically impossible because your brain did not exist before you were born.
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But in a deterministic universe, the creation of my brain was a result of the physical state of the universe prior to my conception and the physical laws that determined my growth. This would extend back to the beginning of this universe, back to the universe that gave birth to this one, and so on and so on.
Present state depends on previous state but not previous states 13 billion years ago.
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You are arguing that somewhere between the present and 13 billion years ago, the universe was not deterministic.
Computer programs predict the flights of spacecrafts.
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The first space shuttle launch aborted at T-13 seconds. For reasons of safety the shuttle had 5 main computers. 4 to calculate using identical programs and one to compare the results. At T-13 the 5th computer detected that the 4 other computers were not in agreement and aborted the launch.
We now know that identical computers do not deliver identical results.
“Bell’s Theorem establishes that there is no hidden variable to tell us which path will be chosen to the future. Thus, our common sense belief that there is only one possible future which is determined by the present and physical laws is false. Therefore the future cannot be determined, except of the basis of probabilities.”
Bell’s theorem describes the behavior of subatomic particles. People and planets are not subatomic particles. Astronomers don’t compute the probability the earth will revolve around the sun this year. Maybe it won’t if a giant comet hit it.
Sorry I’m not interested in philosophical debate. Suffice it to say some phenomena are deterministic, others are not. If you want to believe it’s just one or the other, so be it.
Dolan
I’m referring to Boltzmann’s formulation of the 2nd law. If you’re thinking of Clausius or Kelvin’s formulation, I see why you disagree.
I’m afraid you misunderstood Godel’s theorems. The fact that you’re saying Edward Nelson proved Peano arithmetic to be inconsistent is actually the proof that Godel’s theorems do not apply to Peano arithmetic. The theorems apply to logical systems whose completeness and/or consistency are unprovable. BTW majority of mathematicians accept Gentzen’s proof that Peano’s axioms are consistent. But that’s beside the point.
I do not dismiss relativity theory. It is correct. I merely pointed out that it’s deterministic.
Bell’s theorem describes the behavior of subatomic particles. People and planets are not subatomic particles.
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As demonstrated earlier, your “free will” cannot be distinguished from the actions of a particle. The orbits of the planets are computationally intractable outside of quantum mechanics due to the n-body problem. The exception is the restricted n-body problem, when the planets all lie in the same plane.
Philosophy deals with “Why” something happens. Thus a PhD is a Doctor of Philosophy in her chosen field. Much more interesting and practical are the other 4 W’s. Who, What, When, Where. “Why” can never be answered fully. It is cloaked in the infinity of the universe. Zen provides as good an answer to “Why” as does Science.
I do not dismiss relativity theory.
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Relativity was a giant step forward, combining the work of Newton and Maxwell. The great challenge ahead is to combine Relativity and Quantum Mechanics.
People and planets are not subatomic particles.
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On the contrary, people and planets are all composed of subatomic particles. These provide the illusion of determinism, because of the law of large numbers. While the odds are good that a single particle might wink in or out of existence, the odds are vanishingly small that all the particles that make up planet earth will do this at the same time. QM tells us it is not impossible. Simply very long odds.
I agree with you Nancy. The odds are vanishingly small. That’s why we ignore it. You don’t have to worry that all the atoms in your body will quantum tunnel to a parallel universe.
The present state depends on immediate previous state. Shooting the last snooker ball depends only on the last positions of the two balls. It doesn’t matter how you shot all previous balls. Different snooker games will end the same way so long as the last ball positions are the same.
Dolan
The computers did the celestial mechanics calculations. The astronauts did the flying with the aid of computers. They already have main frame computers in 1960s. Of course that didn’t prevent engineers with slide rules from doing what they love to do. Sir, contrary to your impression, I really don’t care if fire engines are red or green so long as they can put out fires.
Re: free will?
The following is a conclusion from modern information theory. The firing of one of Nancy’s neurons is not conditional upon the firing of those neurons which make synapses with its dendrites. It is conditional upon the PATTERNS of firing of these neurons. That firing is conditional upon patterns of firing is what makes it possible for Nancy to learn. In learning, her brain updates the descriptions of those patterns which produce firing.
Learning provides Nancy with information about the unobserved outcomes of events given the observed conditions that preceed them. By placing her physical self in that condition which predicts the outcome which she desires, Nancy exhibits “free will.”
Were the firing of each of her brain’s neurons to be conditional upon the firing of those neurons that make synapses with its dendrites, Nancy could not exhibit free will. However this proposition is false.
BTW the argument that “the odds are vanishingly small” is also speculative. Real experiments on the famous Schrodinger’s cat paradox revealed that big objects don’t behave like subatomic particles (I’m not surprised). An electron can be in a state of superposition but a cat can never be simultaneously dead and alive (again I’m not surprised)
“Free will is inconsistent with determinism”
Absolutely. Free will is an emergent property of neurons. It cannot be determined by our paltry current understanding.
But is it a quantum property? There is always this issue of scale. Quantum=nano. None of us would argue that the microwaves bouncing off the oxygen molecules telling us the models are out to lunch exist only because we perceive them. Quantum is largely irrelevant at earth scale and human life timeframes. This may be a problem applying quantum/chaos to computer models and climate.
If we were to live our lives by quantum theory, we would all be Post Modern narcissistic nihilists.
The universe is completely deterministic. You can calculate any state and the position of any element at any time, past present, or future. All you need are the complete set of governing principles for the universe, which we don’t quite have just yet, and the initial condition, which we haven’t managed to identify so far.
Once we get those details ironed out, the remaining problem is computational speed. For example, if you want to calculate where, say, a photon will next be, you have to work out the solution faster than the photon can get there. Once you’ve solved the problem of computational speed, it’s all really very easy.
Oh wait… I almost forgot… you also have to have a way of identifying everything in the universe. You don’t want to announce you’ve calculated the next position for Fred the Photon when it was actually Alice the Photon that was zipping by. Alice would not be amused.
Meanwhile, we just do a lot of guesstimating.
(Wonderful essay, Nancy Green. Thank you.)
From a generalist approach to the subject of global environmental perturbations (human and non humanly driven) I understand that our environment has mechanisms of resilience that get activated at local and global scale. Are we aware of those mechanisms? Temperature in our atmosphere can increase due to a number of factors. Greenhouse gases and solar radiation among others. Just playing, the human body uses temperature to react against pathogens. It rises from its balance state giving fever symptoms and this increase triggers the release of water as sweat to absorb the heat through evaporation. Consequently the human body loses water that needs to be replaced. So, in our global ecosystem, there is a debate about if there has been an increase in heat or temperature. Which would be the mechanisms of resilience in our global environment working to absorb or release those increases in heat or temperature (I would go with water as the heat/energy carrier and the weather systems as the physical mechanics to redistribute and release heat/energy. Like stirring a spoon to cold down your soup).
Now, I feel it is very important to understand the mechanisms of resilience at global scale. Which are they? Are they working properly? I don´t think the mechanisms of resilience against increases in temperature due to solar radiation are the same as increases in temperature due to greenhouse gases. Should not reflect such events the ionic charge of the atmosphere? And, would not they be more localised in time (start to finish) than constant heating from inside? (honestly curious) .
So, models can only work with non sporadic events opposite to solar radiation. So, from an anthropogenic point of view, “What about if the global ecosystem has mechanisms of resilience to absorb increases in temperature that makes our correlations weak in time?? Are these mechanisms of resilience being incorporated in our predictive models? The most provably repercussion from activating mechanisms of resilience would be to see cyclic patterns of change. Meaning, e.g. temperature raises, weather patterns would increase performance releasing energy until the atmosphere recovers to a point where to start again. However, the point of starting again might be each time different since the global ecosystem would adapt to the pressure of dominant increasing patterns of temperature. So each time the cycle would start at a higher temperature, inducing an adaptation to the biota to new conditions until the system would adapt to not feeling the perturbation or… the mechanism of resilience does not give a continuous predictable process. One mechanism activates another mechanism due to synergistic effects and so on. So, with each new mechanism activated a new model to be defined. I am not sure about if this is contemplated.
I believe that resilience is playing a mayor role not only in our environment and our understanding when modelling changes in our ecosystem but also in the mindset applied in the debate.
From an environmental point of view I understand that any ecosystem has a limited capacity to absorb perturbations. So, from an hypothetical approach to the subject on human impact versus environmental change I would like to see a case scenario study giving answer to three questions: Could human development have an impact in the ecosystem at global scale? What would have to do humans to alter the ecosystem at global scale? Which part of the ecosystem (soil, atmosphere, light and heat (from our sun), water or living organisms) would reflect primary the impact from human perturbation? In case the answer is “yes” to the first question, how much of the answer for the second and third questions matches with actual facts?
Nancy Green says, “If you live in a deterministic universe then the prior state of the universe determines where you will eat lunch.”
Agreed, which makes the deterministic universe idea uncomfortable.
However, if you live in probabilistic universe, you have no choice either. The place you eat is decided by some grand dice roll, which is an equally uncomforting idea.
A probabilistic universe is equally inconsistent with free will.
“A probabilistic universe is equally inconsistent with free will.”
Very cool. Probabilistic determinism, but emergent properties are wildly improbable. How would you set the odds that consciousness would emerge from neurons when they first evolved in metazoans?
Improbability is the freedom Nancy is talking about. She yearns to find it in chaos, but it clearly arises spontaneously in nature.
A probabilistic universe is equally inconsistent with free will.
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In a deterministic universe there is only 1 future for a given present. There is nothing to choose, because your choice itself is fully determined by physical laws and initial state. What you think is free will is simply an illusion, because your actions are fully determined by your past.
In a probabilistic universe there are many futures possible for a given present. The option exists to choose one of them, in a fashion similar to “Lets make a deal”. You can choose door 1, 2 or 3. But you don’t get to see what is behind the door until after you make your choice.
Another way to think about it is “the future is written”. In a deterministic universe this statement is true, because the future would be fully determined by the present. In a probabilistic universe, the future is not written until you arrive. Until that point it is simply one possibility out of many.
Nancy,
Thank you for the expansion on your ideas. I am learning from you. What I think now is that you believe the following:
1) A probabilistic universe allows for free will, where as deterministic universe world does not.
2) The double-slit (or some other) experiment proves that we live in probabilistic universe.
I would like to ask you to expand on this, not because I believe either is untrue, but because I truly don’t understand the proof. For the record, I also believe that we have free will, and I don’t argue that we don’t live in probabilistic universe. I am simply an agnostic on the latter.
If you have a proof, I can learn from it and would be grateful if you would share it with me. I have an undergraduate degree in physics and a master’s in geophysics, so I should be able to follow your explanation. I am teachable.
There is no need to read further. Here after, I just explain why I am agnostic on the concept of probabilistic universe and why a probabilistic universe does not necessary imply free will.
You write: “In a probabilistic universe there are many futures possible for a given present. The option exists to choose one of them…”. The first sentence, of course, I agree with, but I don’t see any “option”. I assume that you are not saying that we can, through force of will, choose which slot the photon passes through. If that is in our power, one could just as easily, through force of will, alter predetermined outcomes. Either ability is a supernatural power. Why would someone prefer one over the other as an explanation of free will?
Your essay suggests that the macroscopic world we live in is determined by microscopic events. This is a proposition that I would agree with. Hence, not only do microscopic events determine the options that are available to us; they must also determine our decisions. Gymnosperm described my argument as “Probabilistic determinism”. At first, I thought no, but speaking only to the free will issue, yes, one is just swapping one form of determinism for another. If our decision process is determined on a probabilistic microscopic scale, then the dice determine our decisions and our future.
If you can clear up my confusion on that matter, I would be greatly appreciative.
With regards to the issue of the proof of a probabilistic universe, let’s consider the double-slit experiment. At first, flooding the double-slits with light results in a very reproducible diffraction pattern. However, reducing the light intensity and examining closely, we see photons passing through one slot or another in an unpredictable matter. We conclude that an identical experiment yields different results.
However, is it really identical? Let’s look at the “point source”. It consists of millions of atoms/molecules. The probability that any two photos were emitted from the same atom is extremely small.
OK, I’ll do thought experiment with you to resolve the problem. We shall assume that we can isolate a hydrogen atom at zero degrees K (to eliminate thermal motion) and further, we can get the atom to emit photos one after another without disturbing its position. Now from symmetry we can reason that it is equally likely to emit a photon with any trajectory. Therefore, we will only look at photons with identical trajectories, would they pass through the same slot? I’m guessing here, but I would have to say, yes. But now, you say, wait, it is that the atom emits in all direction with equal probability which proves a probabilistic universe.
OK, then I’ll revert to analogy to illustrate my thinking, not to prove a point. This is similar to me arguing that when I miss a golf shot that proves a probabilistic universe. (I think that I’ll use that the next time I miss a putt. Those little windmills ruin my game.)
Back to proof, that we cannot control or predict which trajectory a photon takes, does not prove that is not responding to some physical law in a reproducible manner. I freely admit that is a possibility, but where is the proof?
Re: free will
Free will is a property of entities that are “… guided by cyclical patterns of information flow known as feedback loops.” These are open systems (systems that exchange matter and energy with their environment) that “….maintain and develop structure by breaking down other structures in the process of metabolism, thus creating entropy – disorder – which is subsequently dissipated in the form of degraded waste products.” ( http://www.mountainman.com.au/capra_1.html ). The system of which these entities are a part gains entropy but the entities themselves lose entropy. In doing so, they organize themselves.
I agree with, but I don’t see any “option”.
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In a deterministic universe there is only one future, as determined by current state and physical laws. You have no choice.
In a probabilistic universe there are many futures. The problem you are having is how to select one over the other. How does one make a choice of one future over the other?
I know of no way to do so. You cannot select which path the photon will choose. This is making you feel uncomfortable, because you cannot see the utility.
However, you are asking the wrong question. How can there be any choice if there is only 1 future? With infinite possible futures there is the potential for choice. However, that does not mean that choice is guaranteed.
A better way to think of this is in terms of opportunity. In the probabilistic future all things are possible. In the deterministic future, the future is already written.
While this does not guarantee that you have free will, the double slit experiment (along with Bell’s Theorem) holds forth the possibility that you do have free will. While the deterministic universe provides no opportunity for choice.
For those with a religious background, free will was one of God’s promises to mankind. So, in this respect it appears that religion and science complement each other. That is perhaps one of the greatest accomplishments of quantum mechanics, to provide a first step to reconcile religion and science.
This may be answered already, didn’t get that far.
Alex,
You must have forgot that photons come in different sizes, and they all exhibit this behavior. You can emit a photon from an antenna, and have an exact location for A, and an exact location for B. BTW you can also design your slit to an exact proportion of the wavelength you’re working with in this case.
Momentum is not position.
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Phase space combines position, momentum and time.