When we are doing science we have to start by making assumptions we are confident in: nothing can come from nothing, and nothing just disappears (energy/mass conservation). One even more basic assumption, which I think is where science really has to begin, can be stated this way:
[MP] That which is not observable does not exist.
I call this the materialistic principle, and it is similar to Newton’s Rule 1 for reasoning in philosophy: “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” I have articulated the MP in this way in part because I’m not sure I understand causality. I also want something simple and almost tautological. What I mean is that if anything whatsoever is not observable, and not measurable, then really for no physical model or theory should we pretend it to be there; it would be supernatural, miraculous, magical.
Now, in particle physics and statistical mechanics there exists a principle called indistinguishability. It asserts that there is no way to tell the difference, for example, between one electron and another, or between two photons. That all Helium-3’s are exactly the same, and if I have understood correctly it demands something further: That it is physically impossible to devise any experiment that can distinguish between any two such particles.
That particles actually are indistinguishable I think holds from experimental evidence. The entropy is used extensively to predict the properties of systems of particles. The entropy is related to the number of ways the system can be configured(1). If there were unknown properties that caused the particles to differ from each other, those properties would entail extra degrees of freedom and therefore some contribution to the entropy (2). The accuracy of predictions about the system that require indistinguishability implies that we have completely described the system and its particles.
What are we to do with this? By [MP], I am lead to the hypothesis: Things that are by all observable properties exactly the same, are the same things…
The reason we can’t tell photons apart is because they are, in fact, all the same particle (singular!). That goes for electrons, protons, neutrons, etc.
If I stand in front of a three-way mirror, and you cannot see me directly, but only through my reflections, are there three of me, or only one? Does it depend on how you think about it, and the extent of our experience and expectation? What if all you ever saw were the mirror images, and never actually saw me directly? What would you make of the images?
There are some immediate problems with this, and a lot of confusion, but I am going to struggle through this despite having no resolution for a bit longer because there is an accompanying use of [MP] that will confound and clarify things further. Consider this question:
Is it possible to observe the passage of time without some increase in entropy, or dissipation of some kind occurring somewhere in the system that measures it?
These days there are some very accurate atomic clocks in use. Did you know that a quantum mechanical pendulum really will swing forever, assuming it can be kept from entangling with the exterior environment (read: dissipation, of a sort?). Somehow ‘entropy always increases’ does not apply to quantum mechanics proper. The second law of thermodynamics has to grow out of the quantum mechanical regime in some way that I think is to this day not yet fully described, but is intimately related to problems of coherence (3). The point is that even with a quantum mechanical clock, the device that counts its ticking is necessarily classical and requires some ΔS (entropy increase) of its own.
It follows, and again by [MP], that whenever the system has suffered no increase in entropy, no time can be observed to pass and therefore no time has actually passed.
I can’t go much further than this. I imagine that perhaps the Bing Bang did not occur, or is not located some ‘long time ago’ the way we feebly conceptualize it. I think in a sense we are still inside the singularity, or locked in some (mathematical?) structure that can be described without any recourse to notions of space and time, and in fact from which spacetime can be seen to emerge and give rise to the world of appearances (and mirror images?).
a. In such a Universe, what is causality and how does it arise?
b. We think of entropy as increasing with time, but if entropy is fundamental and time is its consequence, what is the arrow time? How is the apparent passage of time reproduced?
Obviously there are a lot of problems, but there are some things that are easier to swallow, and some problems may become tractable in a description of the universe without space and time as inherent components:
When two particles are in an entangled state and separated by a great distance, and a measurement is performed on one, why does the wave function collapse at the other?
What is the apparent energy which is constant in all space and time, accelerating the galaxies from each other that we call dark energy?
What does the universe look like to a photon?
This last question I have heard was the one that brought Einstein to relativity in the first place, and even now I’m not sure he ever got his answer. If you’ve looked at the equations and studied relativity, you know that lengths will contract for an observer moving at constant speed, and that the equations suffer a singularity when the full velocity of light is reached, i.e, the equations predict that the universe around you, as you approach speed c, will become infinitely squeezed into a plane perpendicular to travel (4). For anything with mass to reach c is forbidden, but what the photon itself sees at c I don’t know, but notice it also predicts that approaching c, time will stop.
- Notice I am not using entropy in the way that is typical in popular science writing, nor am I making explicit reference to any formula. Here I just mean a quantity that is proportional to the logarithm of the number of ways a system can be configured (or might be measured). Here’s a nice video that gives an explanation beyond “order/disorder” without getting too math heavy: http://www.youtube.com/watch?v=vSgPRj207uE
- What if it just so happens that all of the experiments that have been done have never occurred in a regime that allows the particles to access these degrees of freedom? The evidence is not sufficient in that case to show all of the properties are accounted for.
- Coherence, decoherence, entanglement and how the classical world arises from the quantum are all things I am studying and can’t into depth here. I will not linger on this tangent.
- It would take an infinite amount of energy to accelerate anything with mass to the speed of light. It is forbidden for any massless particle (only photons AFAIK, maybe some theoretical ones) to move at any speed other than the speed of light.