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imaginary time

Most such calculations occur in particle physics, in the framework of special relativity, where there are rigorous mathematical proofs showing how the use of imaginary time leads to correct results.

Imaginary time has also been employed in some candidate theories for a theory of quantum gravity, notably in certain types of quantum cosmology. This, however, involves the flexible time of general relativity, and both the details of the imaginary time recipe and the more general question whether or not imaginary time can usefully be employed in this context in the first place are still unresolved, and the object of current research.

Some more information about path integrals and the role of imaginary time can be found in the spotlight text The sum over all possibilities, while imaginary time in quantum cosmology is briefly discussed in Searching for the quantum beginning of the universe.

Definitioner

time

It is a fact of life that not all events in our universe happen concurrently - instead, there is a certain order. Defining a time coordinate or defining time, the way physicists do it, is to define a prescription to associate with each event a number so as to reflect that order - if event B happens after event A, then the number associated with B should be larger than that associated with A. The first step of this definition is to construct a clock: Choose a simple process that repeats regularly. (What is "regular"? Luckily, in our universe, all elementary processes such as a swinging pendulum, the oscillations of atoms or of electronic circuits lead to the same concept of regularity.) As a second step, install a counter: A mechanism that, with every repetition of the chosen process, raises the count by one. With this definition, one can at least assign a time (the numerical value of the counter) to events happening at location of the clock. For events at different locations, an additional definition is necessary: One needs to define simultaneity. After all, the statement that some far-away event A happens at 12 o'clock is the same as saying that event A and "our clock counter shows 12:00:00" are simultaneous. The how and why of defining simultaneity - a centre-piece of Einstein's special theory of relativity - are described in the spotlight topic Defining "now". With all these preparations, physicists can, in principle, assign a time coordinate value ("a time") to any possible events, and describes how fast or how slow processes happen, compared to that time coordinate.

path integrals

Synonym: Sum over histories. A technique for performing calculations in quantum theory. Roughly speaking, the probability for a certain outcome (for instance, a particle reaching location A at time t) is calculated by performing a sum over all possible ways in which this particular outcome can come about. A description of the path integral formulation of quantum theory can be found in the spotlight text The sum over all possibilities.

imaginary time

Certain quantum calculations (notably the calculation of path integrals as a way to find quantum mechanical probabilities) involve an algebraic manipulation of the following kind: Wherever the time coordinate t occurs, it is replaced by i·t, where i is the "imaginary unit", a number defined to have the remarkable property i²=i·i=-1. At the end of the calculation, the substitution is reversed. The combination T=i·t is called imaginary time. Most such calculations occur in particle physics, in the framework of special relativity, where there are rigorous mathematical proofs showing how the use of imaginary time leads to correct results. Imaginary time has also been employed in some candidate theories for a theory of quantum gravity, notably in certain types of quantum cosmology. This, however, involves the flexible time of general relativity, and both the details of the imaginary time recipe and the more general question whether or not imaginary time can usefully be employed in this context in the first place are still unresolved, and the object of current research. Some more information about path integrals and the role of imaginary time can be found in the spotlight text The sum over all possibilities, while imaginary time in quantum cosmology is briefly discussed in Searching for the quantum beginning of the universe.

current

Matter in coordinated, flowing motion - think of water flowing in a pipe. An important example is the electric current associated with moving electric charges. Electric currents are the sources of magnetic fields.

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imaginary time

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