14 April 2013

Are the Planck length and the Planck time fantasies?

There is no chance to ever measure Planck lengths or Planck times. They have no experimental effects whatsoever. Are they useless concepts?

Let me assume for a while that we drop these two concepts. It would mean that we keep quantum theory and gravity separate. We drop unification. What happens? Not much. Quantum theory and particle physics remain valid. Also general relativity remains valid. We know of now experiment that requires both theories at the same time.

In practice, avoiding unification has no effect, because the standard model of particle physics and the concordance model of cosmology agree with all experiments.

So, do we need unification? My answer: yes. We need it to understand the parameters of the standard model and of the concordance model.

Do we need unification for other reasons? My answer: no. But many researchers would answer yes. They add anomalies, instabilities, fine tuning, dark matter and more reasons.

Are the Planck length and the Planck time essential for unification? My answer: just a tiny bit. Other ideas are more important. Is nature really a bowl of noodles? Is nature really a huge gut full of moving intestines? These proposals are, if they are correct, more shocking than the Planck length and the Planck time.


  1. I'm not trying to unfound the Strand Model. I like it! It says 'events and Planck units are crossing switches of featureless strands', but why does it have to be Planck units? Why not 'events and the smallest discernable units of measurement are crossing switches of featureless strands'?

    The minimum action divided by the maximum force and the maximum speed gives a time squared (Planck's unit of time is the square root of that). Well, maximum force times maximum speed gives maximum power, so you've got 'minimum action per maximum power'. When I was reading about action in Schiller's physics books, he said action is basically the measure of change, so you've got 'the smallest measurable change that can happen per maximum power' (and this measure of change is an average over some amount of time). Now, if you've only measured a very small amount of change per unit of power applied even though just one of those units of power amounts to the biggest power possible in the universe, the only explanation is that you must have measured the amount of change over a very, very small amount of time indeed (or else you would have measured lots and lots of change). Great! Now how do we find out what this very small amount of time was? Oh, take the square root. What? Why? What is the reason? Who says it is the only way?

  2. The arguments leading to a minimum time are convincing. And all these arguments lead to the Planck time. There are no reasons to doubt them. But I am curious: why do you doubt them?

  3. Anonymous,

    Nobody knows for sure if the concept of Planck scale is reality or fantasy. The highest energy scale directly probed with particle accelerators is currently at 8 TeV, many orders of magnitude below the Planck length and time. But what we confidently know is that the concept of ultraviolet cutoff is paramount for a consistent understanding of Quantum Field Theory and the Standard Model. The reason has to do with Renormalization Group, a framework that enables sensible predictions in particle physics.

  4. Thank you, Ervin.

    I didn't know that. I looked it up on Wikipedia to find out a bit more about it. I could see the argument for assuming limits above zero and less than infinity, but it didn't say anywhere that the limits used for the purpose had to be Planck units. It seemed to me that you only have to use a limit that is close enough to zero or close enough to infinity that the answer you get agrees with what you observe to within experimental uncertainty. So it looks like you are right that minimum lengths and minimum times are indispensable, but that's not to say that those minimums have been demonstrated to be equal to Planck units. So it's just as you said: 'Nobody knows for sure if the concept of Planck [units] is reality or [nonsense]'.


    Here is my doubt. Say you ask me to calculate the velocity at which I eat my dinner. So I measure the circumference of my plate in metres, and I measure how long I take to eat the dinner from it in seconds. Then I divide my measurement in metres by my measurement in seconds and give you my answer in metres per second. I don't understand the question you asked, and you don't understand the answer I gave, but we both agree the units are correct. How can you tell that Planck units aren't similar nonsense?

  5. Anonymous,

    an answer is nonsene if it is unreasonable. But that is not the case! Have a look at the arguments. In Schiller's volume 6, chapter 3 (pages 52-58), presents the usual argument. It is over 50 years old and so simple that there is not much to doubt. Only two formulas combined.

  6. Thanks, Clara.

    So what it says (among other things) is that the Planck mass unit is the number of kilograms for a point mass whose wavelength and event horizon are the same size.

    Thank you. I've got to go away and have a long think about that (and probably re-read the entire volume 6).

  7. Anonymous,

    the Planck mass and the Planck length are well-established quantities. There really seems little room for alternatives.

  8. Hi, Clara.

    I was thinking about event horizons and wavelengths, and that made me think about Hawking radiation, and it was then that I stumbled upon the 'Trans-Planckian problem' article on Wikipedia. What is the solution to that puzzle?

  9. Anonymous,

    there are no transplanckian quantities. But one can often do as if they existed. When we learn that space is continuous, we assume transplanckian length scales.

    I strongly doubt that the entropy of black holes changes if the transplanckian scales are kept out of the calculation, because its value is itself a limit, like the speed of light.

  10. Thanks, Clara.