Question

(a) A unit of time sometimes used in microscopic physics is the shake. One shake equals \(10^{-8} \mathrm{~s}\). Are there more shakes in a second than there are seconds in a year? (b) Humans have existed for about \(10^{6}\) years, whereas the universe is about \(10^{10}\) years old. If the age of the universe is taken to be 1 day, for how many seconds have humans existed?

Short answer

There are more shakes in a second than there are seconds in a year. If the age of the universe is taken to be 1 day, humans have existed for approximately 8.64 seconds.

Step-by-step solution

Calculate the Number of Shakes in One Second

To calculate the number of shakes in one second, use the given relationship that one shake equals \(10^{-8}\) second. This implies we have \(1/10^{-8} = 10^{8}\) shakes in one second as we reciprocate the value associated with shakes.

Calculate the Number of Seconds in One Year

We know there are 60 seconds in 1 minute, 60 minutes in 1 hour, 24 hours in a day, and 365 days in a year. Multiply all these quantities: \(60 × 60 × 24 × 365 = 31536000\) seconds in one year.

Compare the Number of Shakes in a Second and Seconds in a Year

By comparing \(10^{8}\) shakes and \(31536000\) seconds, it's clear there are more shakes in a second than there are seconds in a year.

Calculate the Age of Humans in Universe Day

The age of the universe is given as \(10^{10}\) years and taken to be 1 day. The age of humans is given as \(10^{6}\) years. By creating a proportion we can determine the age of humans in universe day. That is, \((10^{6} ÷ 10^{10}) × 1 = 10^{-4}\) universe days.

Convert Universe Day into Seconds

We know there are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute, multiply all these to convert universe day into seconds: \(10^{-4} × 24 × 60 × 60 = 8.64\) seconds.

Key concepts

Microscopic Physics Time Units

Understanding time at a microscopic level is critical in physics, particularly when studying the interactions of subatomic particles or the vibrations of atoms within materials. One specialized time unit used in these contexts is the 'shake'.

A shake represents a very short period of time which is equivalent to ten billionths of a second, or more precisely, \(10^{-8}\) seconds. To contextualize this, consider the rapidity of nuclear reactions and other subatomic processes that occur within such a minuscule interval. When we think about our everyday experience, a second seems fleeting, but within a second, there are a staggering \(10^8\) shakes!

Imagine a tiny particle zipping through space—it might be engaged in millions of interactions within the blink of an eye, which is why scientists need such small time units to accurately measure and describe these events.

Calculating Shakes in Physics

Calculating shakes and understanding their relevance in physics can be an eye-opening exercise. The term 'shake' might evoke the idea of something moving back and forth quickly, and in the domain of physics, it captures the essence of events that happen incredibly fast.

Based on the definition that one shake is equivalent to \(10^{-8}\) seconds, the number of shakes in a single second is simply the inverse of this, resulting in \(10^8\) shakes per second. This immense figure underscores the utility of the shake; it is an efficient way of breaking down the second for use in calculations involving brief phenomena, like those in nuclear physics.

To actually calculate the number of shakes that occur over a span of time, one would divide the total time in seconds by \(10^{-8}\), providing a count of these fleeting intervals within the specified duration. This also means that in events or systems where timing needs to be incredibly precise, such as in the detection of particle decays or the timing of pulsars, the shake becomes an indispensable tool in a physicist's toolkit.

Age of Universe Calculation

The age of the universe is a topic that can easily boggle the mind, with its vast scales of time stretching far beyond human history. It's estimated that the universe is approximately \(10^{10}\) years old, a number with ten billion years worth of seconds, minutes, and millennia. In contrast, the span of human existence is believed to be around \(10^{6}\) years.

By scaling down the age of the universe to fit within the framework of a single 24-hour day for easier conceptualization, each 'universe year' represents a significantly condensed amount of real-time. If the age of the universe is represented by 1 day or 24 hours, the entire length of human history can be distilled into mere seconds.

By calculating this proportion, we find that humanity has been around for approximately 8.64 seconds of this 'universe day', a fleeting moment when compared to the vast expanse of cosmic history. This imaginative exercise not only aids in grasping the enormity of cosmic time scales but also highlights the relative infancy of human civilization in the grand scheme of the universe.