For a course I am teaching, I am rereading a biography of Einstein (written by Walter Isaacson) and I would like to share a frustration with you.
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Are We Sure The Universe Started With A Big Bang?
Personal –
I started my studies at the university doing astrophysics, because I wanted to understand everything – from the smallest molecule to the largest galaxy. It wasn’t long before I discovered that, as an astrophysicist, you spend most of your time struggling with computer-code and staring at computer screens, because the data coming from telescopes is too complex for humans to handle.
What I also found difficult to swallow, is the ease with which astrophysicists seem to accept wildly speculative theories. An example of such a theory is the Big Bang Theory.
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The Quantum Vacuum And The Cosmological Constant
Connectedness
You haven’t heard from me in a while because I was down with the flu followed by a serious wound infection. It was serious, because the blood-flow through my left body-half is slow due to my braintumor – which makes it difficult for my immune system to fight bacteria. Luckily, a week of antibiotics was enough to fight off the infection.
As I was recovering, I had to save my energy, so there wasn’t much I could do besides lying in bed and thinking. At such moments (when the pain is not too bad), I often marvel at the connectedness of everything I see around me.
At one point I was looking out my window, at a clear blue winter sky, and I was reminded of Carlo Rovelli’s article “Space is blue and birds fly in it“. Moments like this remind me that abstract concepts like Einstein’s space and time not only exist in theoretical physics, but they are everywhere around us – the clear blue winter sky is actually the expanding deep space of Rubin, Hubble and Lemaitre – the space Einstein once believed to be characterized by the cosmological constant.
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How Can Dimensions Be Hidden?
How can a dimension be hidden?
Extra dimensions pop up everywhere in physics. From string theory to attempts at unifying general relativity with quantum theory. But how can it be that we can’t see them?
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Extra Dimensions Could Explain Entanglement
We can understand quantum entanglement if particles in our 3-dimensional space are actually strings in a 4-dimensional space.
One of the most counterintuitive aspects of quantum mechanics is entanglement: We have seen in experiments that there are correlations between events that are far away from each other – so far, in fact, that no signal or anything else can travel from one to the other to cause the correlation. Words cannot express how bizarre this is (although Einstein came a long way when he called this “spooky action at a distance”)*.
But what if the universe has four spatial dimensions of which we are aware of only three? Could points in space we think of as far away from each other actually be connected through some invisible, higher dimension?
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The Paradox Of The Arrow Of Time
“Do not try and solve the paradox; that’s impossible. Instead, only try to realize the truth… there is no paradox.”*
Why is there a difference between past and future?
The laws of Newton are symmetrical in time while the entropy of a closed system always increases – creating an arrow of time. How can it be that the laws describing particles are the same whether we go forward or backwards in time, while a law describing the same system macroscopically is very different in terms of past and future?
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Why Is There No Sound Postulate?
In physics, the speed of a wave is defined independently from the speed of its source.
Then why did Einstein say that the speed of lightwaves is independent of their source – why not claim that the speed of any wave is independent of its source?
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A derivation of the Minkowski metric
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A derivation of the Lorentz equations
For a future blog post I’m working on, I would like to show how the Lorentz transformations are derived. To remind you, the Lorentz transformations tell us how variables change when we go from one reference frame to another one that is moving relative to the first.
We start in a reference frame S, in which there is only one spatial dimension, $x$. Now compare S with a reference frame S’ moving with velocity $v$ in a positive $x$ direction. How do we relate $x$ and $t$ in S to their equivalents $x’$ and $t’$ in S’?
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Trains, clocks and lightspeed
Yesterday I received an email with a very interesting question about Einstein’s lightclock. Why do we assume that light in a moving lightclock travels a longer distance than in a clock that stands still? If we throw a ball into the air in a moving train, it falls down vertically, right? Why is that different for a clock? This is a great question! It helps us realise what it actually means to say that things happen in absolute space (as Newton believed).
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