Can relativity theory be reconciled with common sense?

 You might think I write enough posts on Einstein’s theories of relativity, including the last one, but this one is less esoteric. It arose from a question I answered on Quora. Like a lot of questions on Quora, it’s provocative and you wonder whether the questioner is serious or not.
 
Before I came up with the title, I rejected 2 others: Relativity theory for dummies (which seemed patronising) and Relativity explained without equations or twins (which is better). But I settled on the one above, because it contains a thought experiment, which does exactly that. It’s a thought experiment I’ve considered numerous times in the past, but never expressed in writing.
 
I feel that the post also deals with some misconceptions: that SR arose from the failure of the Michelson-Morley experiments to measure the aether, and that GR has no relationship to Newton’s theory of gravity.
 
If the theories of relativity are so "revolutionary," why are they so incompatible with the 'real' world? In others(sic), why are the theories based on multiple assumptions in mathematics rather than the physical world?
 
You got one thing right, which is ‘theories’ plural – there is the special theory (SR) and the general theory (GR). As for ‘multiple assumptions in mathematics’, there was really only one fundamental assumption and that determined the mathematical formulation of both theories, but SR in particular (GR followed 10 years later).
 
The fundamental assumption was that the speed of light, c, is the same for all observers irrespective of their frame of reference, so not dependent on how fast they’re travelling relative to someone else, or, more importantly, the source of the light. This is completely counter-intuitive but is true based on all observations, including from the far reaches of the Universe. Imagine if, as per our common sense view of the world, that light travelled slower from a source receding from us and faster from a source approaching us.
 
That means that observing a galaxy far far away, the spiral arm travelling away from us would become increasingly out-of-sync with the arm travelling towards us. It’s hard to come up with a more graphic illustration that SR is true. The alternative is that the galaxy arms are travelling through an aether that permeates all of space. This was the accepted view before Einstein’s ‘revolutionary’ idea.
 
True: Einstein’s idea was premised on mathematics (not observation), but the mathematics of Maxwell’s equations, which ‘predicts’ the constant speed of light and provides a value for it. As someone said (Heinrich Hertz): “we get more out of [these equations] than was originally put into them.”
 
But SR didn’t take into account gravity, which unlike the fictitious aether, does permeate the whole universe, so Einstein developed GR. This was a mathematical theory, so not based on empirical observations, but it had to satisfy 3 criteria, established by Einstein at the outset.
 
1)    It had to satisfy the conservation laws of energy, momentum and angular momentum
2)    It had to allow for the equivalence of gravitational and inertial mass.
3)    It had to reduce mathematically to Newton’s formula when relativistic effects were negligible.
 
Many people overlook the last one, when they claim that Einstein’s theory made Newton’s theory obsolete, when in fact, it extended it into realms it couldn’t compute. Likewise, Einstein’s theory also has limitations, yet to be resolved. Observations that confirmed the theory followed its mathematical formulation, which was probably a first in physics.

Note that the curvature of spacetime is a consequence of Einstein’s theory and not a presupposition, and was one of the earliest observational confirmations of said theory.
 
 
Source: The Road to Relativity; The History and Meaning of Einstein’s “The Foundation of General Relativity” (the original title of his paper) by Hanoch Gutfreund and Jurgen Renn.
 

Addendum: I elaborate on the relationship between Newton's and Einstein's theories on another post, in the context of How does science work?

The fabric of the Universe

Brian Greene wrote an excellent book with a similar title (The Fabric of the Cosmos) which I briefly touched on here. Basically, it’s space and time, and the discipline of physics can’t avoid it. In fact, if you add mass and charge, you’ve got the whole gamut that we’re aware of. I know there’s the standard model along with dark energy and dark matter, but as someone said, if you throw everything into a black hole, the only thing you know about it is its mass, charge and angular momentum. Which is why they say, ‘a black hole has no hair.’ That was before Stephen Hawking applied the laws of thermodynamics and quantum mechanics and came up with Hawking radiation, but I’ve gone off-track, so I’ll come back to the topic-at-hand.
 
I like to tell people that I read a lot of books by people a lot smarter than me, and one of those books that I keep returning to is The Constants of Nature by John D Barrow. He makes a very compelling case that the only Universe that could be both stable and predictable enough to support complex life would be one with 3 dimensions of space and 1 of time. A 2-dimensional universe means that any animal with a digestive tract (from mouth to anus) would fall apart. Only a 3-dimensional universe allows planets to maintain orbits for millions of years. As Barrow points out in his aforementioned tome, Einstein’s friend, Paul Ehrenfest (1890-1933) was able to demonstrate this mathematically. It’s the inverse square law of gravity that keeps planets in orbit and that’s a direct consequence of everything happening in 3 dimensions. Interestingly, Kant thought it was the other way around – that 3 dimensions were a consequence of Newton’s universal law of gravity being an inverse square law. Mind you, Kant thought that both space and time were a priori concepts that only exist in the mind:
 
But this space and this time, and with them all appearances, are not in themselves things; they are nothing but representations and cannot exist outside our minds.
 
And this gets to the nub of the topic alluded to in the title of this post: are space and time ‘things’ that are fundamental to everything else we observe?
 
I’ll start with space, because, believe it or not, there is an argument among physicists that space is not an entity per se, but just dimensions between bodies that we measure. I’m going to leave aside, for the time being, that said ‘measurements’ can vary from observer to observer, as per Einstein’s special theory of relativity (SR).
 
This argument arises because we know that the Universe is expanding (by measuring the Doppler-shift of stars); but does space itself expand or is it just objects moving apart? In another post, I referenced a paper by Tamara M. Davis and Charles H. Lineweaver from UNSW (Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe), which I think puts an end to this argument, when they explain the difference between an SR and GR Doppler shift interpretation of an expanding universe.
 
The general relativistic interpretation of the expansion interprets cosmological redshifts as an indication of velocity since the proper distance between comoving objects increases. However, the velocity is due to the rate of expansion of space, not movement through space, and therefore cannot be calculated with the special relativistic Doppler shift formula. (My emphasis)
 
I’m now going to use a sleight-of-hand and attempt a description of GR (general theory of relativity) without gravity, based on my conclusion from their exposition.
 
The Universe has a horizon that’s directly analogous to the horizon one observes at sea, because it ‘moves’ as the observer moves. In other words, other hypothetical ‘observers’ in other parts of the Universe would observe a different horizon to us, including hypothetical observers who are ‘over-the-horizon’ relative to us.
 
But the horizon of the Universe is a direct consequence of bodies (or space) moving faster-than-light (FTL) over the horizon, as expounded upon in detail in Davis’s and Lineweaver’s paper. But here’s the thing: if you were an observer on one of these bodies moving FTL relative to Earth, the speed of light would still be c. How is that possible? My answer is that the light travels at c relative to the ‘space’* (in which it’s observed), but the space itself can travel faster than light.
 
There are, of course, other horizons in the Universe, which are event horizons of black holes. Now, you have the same dilemma at these horizons as you do at the Universe’s horizon. According to an external observer, time appears to ‘stop’ at the event horizon, because the light emitted by an object can’t reach us. However, for an observer at the event horizon, the speed of light is still c, and if the black hole is big enough, it’s believed (obviously no one can know) that someone could cross the event horizon without knowing they had. But what if it’s spacetime that crosses the event horizon? Then both the external observer’s perception and the comoving observer’s perception would be no different if the latter was at the horizon of the entire universe.
 
But what happens to time? Well, if you measure time by the frequency of light being emitted from an object at any of these horizons, it gets Doppler-shifted to zero, so time ‘stops’ for the ‘local’ observer (on Earth) but not for the observer at the horizon.
 
So far, I’ve avoided talking about quantum mechanics (QM), but something curious happens when you apply QM to cosmology: time disappears. According to Paul Davies in The Goldilocks Enigma: ‘…vanishing of time for the entire universe becomes very explicit in quantum cosmology, where the time variable simply drops out of the quantum description.’ This is consistent with Freeman Dyson’s argument that QM can only describe the future. Thus, if you apply a description of the future to the entire cosmos, there would be no time.
 
 
* Note: you can still apply SR within that ‘space’.

 

Addendum: I've since learned that in 1958, David Finkelstein (a postdoc with the Stevens Institute of Technology in Hoboken, New Jersey) wrote an article in Physical Review that gave the same explanation for how time appears different to different observers of a black hole, as I do above. It immediately grabbed the attention (and approval) of Oppenheimer, Wheeler and Penrose (among others), who had struggled to resolve this paradox. (Ref. Black Holes And Time Warps; Einstein's Outrageous Legacy, Kip S. Thorne, 1994)