A goldfish can generally survive without food for around two weeks in optimal conditions. However, there are many factors that can influence this timeframe, such as the water temperature, quality, and the goldfish's overall health.
Goldfish, like most organisms, need food to survive. Under regular feeding conditions, a healthy goldfish may be fed once to twice a day. However, goldfish are also known to be capable of withstanding relatively prolonged periods without food. That said, going two weeks without food is generally considered the maximum time a goldfish can survive without significant health risks.
The ability of goldfish to survive without food for this long can be attributed to their nature as cold-blooded creatures. With a slower metabolism compared to warm-blooded animals, cold-blooded creatures like goldfish can survive without food longer as they do not burn energy as quickly. Also, goldfish naturally graze on algae and other materials in their environment when available - hence, even without their typical feed, they might find alternative sources of nutrition.
Water temperature plays a role as well: a lower temperature slows down the fish's metabolism, resulting in slower consumption of their energy reserves. So, goldfish in cooler water may survive a little longer without food than those in warmer water.
Conversely, a period of excessive hunger can drastically impact a goldfish's health. Extended starvation can lead to a weakened immune system, making the fish more susceptible to diseases. Also, a protein deficiency can lead to stunted growth and deterioration of the tissues, among other problems. Fat, muscles, and other body tissues may be consumed by the body as a last-resort energy source, causing further harm and potentially leading to death.
To summarize, while a goldfish can survive without food for two weeks, it is crucial to understand that survival does not equate to optimal health or well-being. Regular feeding of a well-balanced diet promotes the overall health, longevity, and happiness of a pet goldfish. If you know in advance that you won't be there to feed your pet for a week or more, it may be best to arrange for a friend, neighbor, or pet sitter to take over the feeding duties.