I think the ideas of relativity, in particular the ideas of space and time having no absolute physical meaning are completely confounding to my human ideas of space and particularly time as absolute. As a physicist, I can “in my head” perfectly appreciate how this all works in relativity, but this intuition and my human conceptions of space and time as absolute just don’t get on at all! In particular, I find it incomprehensible that different observers can perceive different rates of flow of time between the same pair of events; to the physicist this is just the norm, but to my naive intuition it’s just unimaginable how to reconcile this with the fact that I inextricably perceive one physical reality, one notion of time, that my subconscious resolutely maintains that this must be the same for everyone.
In quantum mechanics, the best we can ever do with “initial conditions” is predict with what probabilities we’ll measure particular outcomes in experiments. This is essentially a non-deterministic picture of physical reality, in which one’s common intuition of a kind of clockwork/cause-effect universe just drops dead. Whilst we can understand, deterministically, how the probability distributions pertaining to the likelihood of certain outcomes evolves, we cannot, even in principle identify exactly what causes an event to happen or not! In short, the universe rolls the dice and things just happen! In this picture too the common ideas of what it means for something to be solid, or even have a size at all, break down. This is due again to the fundamentally probabilistic nature of quantum mechanics. For instance, let me try to define the size of the electron in an absolute fashion. Now the best I could ever do is to tell you with what probability I might find the electron in a given region. I could say something like “there’s a greater than 99% chance of finding it in this region, so I’ll call the size of this region the size of the electron”. Now this is fine, but clearly it’s not a canonical definition, since I can choose any threshold that I like. the bottom line is that it doesn’t really have a size! Throw in the double-slit experiment and your intuition of particles as being fundamentally anything like what one normally thinks of as particle-like (something like a billiard ball with a definite size etc.) is turned completely on it’s head; the weirdness of quantum mechanics leaves little to no room to accommodate our everyday intuition! Again, extremely compelling experimental evidence forces us to accept this physical picture concerning the “physics of extremely tiny scales”.
All in all I think it's the profoundly discordant interplay between the world unveiled by the progress of modern theoretical physics and my limited human conception of the world that I inhabit in my day-to-day existence. I strongly suspect that there’s a large part of my subconscious that, largely unbeknownst to me, doesn’t even believe that these competing ideas even refer to the same thing, and that physics just describes a kind of fantastical world! The strangest thing about all of this is that these utterly insane-souding ideas with all of their abstract philosophical baggage are all very, very real, by which I mean that these descriptions of the physical world have time again been experimentally shown to provide the most accurate descriptions of the physical world that we have!
To me this all redounds to the extremely limited perspective of everyday thinking and the fact, that we must all face, that it bares little to no relevance to the physical world we observe in generality. Indeed, the universe is under no obligation whatsoever to be easily understood by anyone, no matter what all manner of branches of wishful thinking in human thought have to say on the matter.
The uniformity of the cosmic microwave background. The universe is 14 billion years old, and light coming from the left, 14 billion light years away, and from the right, 14 billion light years away, shows nearly identical spectral properties. They never communicated. How could that be?
That quandary led me into cosmology. Now we have a tentative answer for the question, based on the theory of inflation, which posits an early phase of the universe in which the size of the universe expanded at an equivalent rate that far exceeded the speed of light. Needless to say, even though that theory may be right, it continues to stretch not only space but also my mind.
Another example is entanglement, the mysterious covert action at a distance that is part of the present understanding of quantum physics. It appears to violate an inviolable principle of relativity — that nothing can affect distant phenomena at a speed greater than that of light; yet experiments verify that it is true.
And finally, the flow of time. This is not truly strange; it is part of our everyday lives. What is strange is that it is not yet part of physics. The equations of physics ignore the existence of that most important of all time moments, “now”. Quote from my book Now: The Physics of Time.
“The elusive meaning of now has been a stumbling block in the development of physics. We understand time dilation from velocity and gravity, even the flipping of time in relativity theory, yet we’ve made no progress in explaining the most striking aspects of time: its flow and the meaning of now. The basic drawing board of physics known as a space-time diagram ignores these issues, and physicists sometimes perversely treat this absence as a strength and conclude that the flow of time is an illusion. That’s backward. As long as the meaning of now eludes us, further advances in understanding time—that key aspect of reality—will continue to be stalled.”
Most physicists are amazed by quantum mechanics when they first encounter it. And quite rightly so. Many-worlds interpretation
Some other things :
- Cantor's theorem and the infinite hierarchy of infinities. Cantor's diagonal argument
- Ghost particles. They only exist as virtual particles, never real particles. How can that be? Faddeev–Popov ghost
There are so many things…the obvious ones for almost any physicist would be learning Quantum Mechanics and General Relativity. They both have sufficiently strange - from our perspective - consequences that every experimental or observational verification of each still seems implausible every time.
These days, though, I am often shocked by mathy things. For example, the Bailey–Borwein–Plouffe formula. How is that even possible?
Disclaimer: I am not a physicist but wished I was at times.
1. Quantum Entanglement: “spooky action at a distance”
The entangled particle appears to know the state of each other at an arbitrary distance. If one observes that one pair of particle has clockwise spin, the other particle will have counter clockwise spin guaranteed. This will hold true at any distance even at light years apart.
We must have missed something really fundamental about how the universe really works.
2. Observable universe (topology of the universe)
That you cannot see stars (or galaxies) beyond the observable boundary. Why is it finite as it seem without a physical boundary?
3. Why is universe not absolutely perfectly homogeneous?
If Big Bang started out as a dimensionless point, what information has caused expanding matters to be unevenly distributed so that they clump together later.
4. Accelerating expansion of the universe
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