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What exactly is energy debt and why does not having energy debt mean that particles and antiparticles don't instantly annihilate each other.

I'm struggling to understand why this happens (quote from a book):

By 10^-32 seconds, the separation of forces had boosted the temperature from zero back to 10^28 degrees again, and flooded the universe with energy. So when virtual particle and antimatter particle came into being, there was no need to pay of the energy debt by instantly annihilating

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  • $\begingroup$ Which book is the source of your quotation? $\endgroup$ – rob May 23 '18 at 14:26
  • $\begingroup$ @rob Big Bang. Couper, Heather; Henbest, Nigel $\endgroup$ – MinecraftBoxGuy May 24 '18 at 15:52
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It comes from the energy-time form of the Heisenberg uncertainty relation. $\Delta E \Delta T \geq {\hbar \over 2}$. If a state persists for a short period of time then the energy is uncertain (and the shorter the state the larger the energy uncertainty) so the conservation of energy can't be applied.

An example often used is of someone working in a shop or bar who borrows money from the till and puts it back. If they walk off with a small sum they don't have to restore it till the books are done at the end of the month: if it's a large sum then they have to get it back pretty quick or the boss will notice. This is an easy-to understand analogy but I'm not convinced about its correctness - let alone its morality.

Using this picture, a virtual particle-antiparticle pair can be created from nothing - despite the need to provide energy $2mc^2$ if these were real particles - provided they annihilate again within a time smaller than $\hbar / 4 m c^2$. This can be called `paying off the energy debt' - though the analogy is being pushed perhaps further than it merits.

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  • $\begingroup$ Thank you! Is there any reason that the particles wouldn't annihilate each other, when there is a lot of energy, like in the Big Bang? $\endgroup$ – MinecraftBoxGuy May 17 '18 at 5:30
  • $\begingroup$ They can annihilate - but they can also do a lot of other things. $\endgroup$ – RogerJBarlow May 17 '18 at 9:25

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