# Does the calculated large cosmological constant in falsify QFT?

1. Dec 13, 2008

### ensabah6

QFT it is possible to calculate the energy density of empty space.

It is known to be around 10^50 orders to large.

Does the calculated large cosmological constant in falsify QFT?
Or does GR have to be re-done with a higher energy density

2. Dec 13, 2008

### vanesch

Staff Emeritus
That value is obtained by taking the +1/2 hbar . omega term in each mode and consider all possible modes up to some cutoff like the Planck length. As such, you get an incredibly high energy density.

Of course, as general relativity allows for a cosmological constant which has about the same function, one could say that this cosmological constant sets off exactly in the opposite direction so that the net effect is what we happen to find as a background density. But that begs the question of how it could happen that there is such a "fine tuning" of both.

The usual trick that is done in this case is to postulate "normal ordering" of the operators, which amounts to putting the +1/2 hbar.omega term in the dustbin. However, in how much this is something deep, and in how much this is a cheap mathematical trick to get rid of it, can be debated.

Probably you have to think of it as this way: QFT is not the right theory to try to estimate the energy density of the vacuum (which only plays a role when general relativity is in the game, which isn't included in QFT in the first place). In other words, calculations of the energy density of the vacuum fall outside of the scope of validity of QFT as we usually know it. A bit like saying that calculating emission spectra of atoms falls outside of the scope of Newtonian mechanics.

You might be shocked to learn that that most sophisticated theory, QFT, has things "outside of its scope". Well, to paraphrase Witten (or was it Schwarz ?) half jokingly: with a $1,- experiment, you already show something that is not explained by QFT: take a cheap pen. Drop it. See it fall. There you are. (in fact, this is from memory, and he said something like "with a$1,- experiment, you can show something that string theory predicts...)

3. Dec 13, 2008

### Fredrik

Staff Emeritus
All the QFTs start with the assumption that spacetime is Minkowski space, which is the solution of Einstein's equation that you find by first assuming that the universe is completely empty and that the density of vacuum is exactly zero. Then you introduce fields that "live" in this spacetime, without affecting its geometry. A non-zero density of vaccum is completely irrelevant in this theory since we have postulated that nothing can change the geometry. So it shouldn't be too surprising that these theories make absurd predictions about the density of vacuum.

Another way of estimating the QFT density of vacuum is to note that the density can be non-zero and that nothing can give us a much better estimate of its value than a simple order-of-magnitude estimate obtained from dimensional analysis of the fundamental constants. You just guess that the density is $\hbar^ac^bG^c$ and then you choose a, b and c, so that the units of this quantity is kg/m3.

The result is more like 10120 larger than the observed value.

4. Dec 13, 2008

### Haelfix

It depends how you want to count.. Its really a quartically divergent quantity so you could say its more like 1 part in 10^34. And then Susy cuts it in half logarithmically.

Ultimately the problem is only manifest in field theory when you turn on gravity, otherwise you were always free to set a zero (typically one just subtracted off the entire vacuum energies contribution).

But once gravity is included, its semi obvious that something is going very wrong with our naive guesses in the quantum gravity regime, and well that story has yet to be written.

5. Dec 13, 2008

### ensabah6

interesting. Is it possible QFT calculations are correct and GR has to and can be modified to accommodate QFT values for vaccuum energy?

Does SUSY and string theory improve the situation?

6. Dec 14, 2008

### vanesch

Staff Emeritus
That's what people are trying to find out for some 30 years or so

7. Dec 15, 2008

### Demystifier

The cosmological constant is not the only thing wrongly predicted by QFT. In fact, QFT predicts that ANY effective parameter is too large when loop contributions are taken into account. But then, of course, it is renormalization that saves the situation. Renormalization of the cosmological constant is not much different from, e.g., renormalization of the electron mass.

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