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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Euclid’s parallel Postulate
Non-Euclidean Geometry
Today I started a lecture series about Einstein’s relativity theories. I started explaining things about basic geometry, so we talked about the postulate of the parallels first described by Euclid of Alexandria: if you draw a straight line on a piece of paper (l in the image on the right) and a point (p in the image) next to it, then there can be only one straight line through this point which does not intersect the line we started with (the dashed line) – there is only one parallel.
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Is information physical?
Recently I visited a conference at the university of Delft dedicated to quantum technology and philosophy. Among physicists working with quantum information, it has become more and more fashionable in the past few decades to say that information is physical. Is that a sensible claim?
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Hoe de Riemann tensor gekromde ruimte beschrijft
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