Novel Quantum Theory Detector Circuit

QUANTUM THEORY DETECTOR THE CIRCUIT The quantum theory detector works similarly to the Schrödinger’s cat analogy of how light can exist as particles and as waves. The two alternating LEDs in the circuit are representative of Schrödinger’s cat’s state - it can be dead, or alive, or dead and alive at the same time (according to quantum theory). Because of the way the circuit is constructed, the two LEDs can never be switched on at the same time, just like outside of the quantum realm, a cat cannot be dead and alive at the same time. However, in the impossible instance that the two LEDs did become switched on at the same time, the buzzer would sound. So the purpose of the circuit concept is that it can be placed inside a cardboard box (like Schrödinger’s cat) so that nobody can see inside, while the two LEDs alternate being switched on and off. It’s called a quantum theory detector because the buzzer would sound in the event that a quantum instance occurred inside the cardboard box, in order to alert bystanders. Circuit Diagram: R1 330Ω

R2 10kΩ

R3

R4 330Ω

10kΩ

R5 LED1

S

LED2 C1 100µF

2kΩ

C2 100µF

+9V

T2

T1

Bt R6

100Ω

R7

74LS00 IC

Bz

IC

100Ω

Bt

9V battery to supply the circuit with enough electricity to power all the components.

S

Switch that allows the circuit to be turned on and off.

R1 and R4

330Ω resistors that protect the LEDs from being destroyed by current overload.

R2 and R3

10kΩ protective resistors for the capacitors so they don’t charge too quickly. They also protect the transistors from current overload through the base.

LED1 and LED2

Light emitting diodes that take turns to light up when their corresponding transistors are switched on.

© Sarah Don, Australia, 2008

C1 and C2

100µF capacitors which are the main components in the two timing circuits that make the LEDs alternate on and off. While C1 is charging, C2 is discharging which provides a current through the base of T1 which turns of LED1. LED1 stays lit up until C2 has discharged enough so that the voltage through the base of T1 is less than 0.6V (the minimum voltage for the transistor to be switched on). When T1 switches off, LED1 switches off and the situation is reversed so that C2 begins to charge up and the cycle begins again.

T1 and T2

Transistors that act as switches to allow the capacitors to take turns to charge and discharge, allowing the LEDs to oscillate.

R6 and R7

100Ω resistors that provide a voltage rise between the transistor and 0V rail so that the integrated circuit (IC) can pick up the high and low voltage signals.

R5

The battery provides the circuit with 9V but the IC can only handle 5V so R 5 drops the voltage and thus acts as a protective resistor for the IC.

IC

Integrated circuit consisting of four NAND gates. In order to translate two high signals into a high signal (if the two LEDs were ever switched on at the same time, causing current to flow through both transistors), the IC has to behave as an AND gate. An AND gate can be made by putting two NAND gates together as shown in table 1 and figure 2. Table 1 – Truth tables of AND and NAND gates

A 0 0 1 1

B 0 1 0 1

NAND 1 1 1 0

Figure 2 – Signal translations

AND 0 0 0 1

1 1

0

0

1

0

The integrated circuit requires ~5V to work and the logic gates require a voltage rise of 2 volts in order to detect a signal above other interference. Bz

Buzzer that sounds when the IC outputs a high signal indicating that both LEDs are switched on at the same time. So, in practise, the buzzer should never sound. However, in order to make sure that the buzzer is actually working, a short circuit test can be done. By connecting the two inputs into the first NAND gate together, the NAND gate should produce a high signal, causing the buzzer to sound.

Each of the components in the circuit has its own important part to play in making the circuit work as a whole. Certain components have voltage and current limits, which when reached, could damage the component. If one of the components, for example a transistor, is damaged then the current would not flow through the correct paths and the timing circuit would fail. The following investigation is specific to the role of capacitors within the quantum theory detector.

© Sarah Don, Australia, 2008

EXPERIMENTAL INVESTIGATION Aim: To investigate the relationship between the frequency at which the LEDs oscillate on and off and the capacitance of the capacitors. Hypothesis: As the capacitance of the capacitors increases, the LEDs oscillate slower. Safety:  

An electric shock may be experienced if the 9V battery is short-circuited through the body. Short-circuiting the capacitors or transistors may cause them to burn or explode.

Materials:      

   

2x 330Ω resistor 2x 100Ω resistor 2x 10k Ω resistor 2k Ω resistor 2x LED 2x transistor

330Ω

13x connecting wires 9V battery 74LS00 integrated circuit Micro-lab Electronics breadboard Buzzer



10kΩ

10kΩ

  

Switch Stopwatch 2x assorted capacitors (47µF, 100µF, 220µF, 330µF, 470µF)

330Ω

2kΩ

100µF

100µF

+9V 74LS00 IC

100Ω

100Ω

Diagram 1 – Setup of circuit

© Sarah Don, Australia, 2008

Method: 1. The circuit was constructed as shown in Diagram 1. 2. The pair of 47µF capacitors was inserted into the circuit and the number of flashes in one minute for a single LED was recorded using a stopwatch. 3. Step 2 was repeated for each of the other pairs of capacitors (100µF, 220µF, 330µF, 470µF). 4. The time between flashes was found by dividing 60 (seconds) by the number of flashes for each capacitor found in step 3. 5. For the purpose of accurate measurement, the highlighted sections of the circuit in diagram 2 were virtually recreated using Crocodile Physics as shown in diagram 3, with the initial capacitance of the capacitor at 47µF, the resistor set at 10kΩ and the battery supplying 9V. (The LED was just an indicator that the capacitor was actually discharging. It is not representative of either of the LEDs in the quantum theory detector circuit).

47µF

Diagram 2 – Capacitor and resistor

Diagram 3 – Simple circuit in Crocodile Physics (capacitor charging)

6. The capacitor was linked with the graphing function in Crocodile Physics to graph voltage against time. 7. The circuit was switched on to charge the capacitor and then short-circuited to discharge the capacitor while the graph recorded the change in voltage to obtain a graph as shown in diagram 3.5. 8. Steps 4-7 were repeated with the pairs of 100µF, 220µF, 330µF and 470µF capacitors in the Crocodile Physics program.

Diagram 3.5 – Graph of capacitor charging and discharging using Crocodile Physics (the charge time is from 0-2 seconds and the discharge time is from 3.2-3.6 seconds).

Results: Table 4 – Capacitance’s affect on LED oscillation and the charge and discharge time of capacitors Capacitance LED flashes per Time of LED Charge time Discharge time minute oscillation (seconds) (seconds) (seconds) (µF) 47 140 0.43 2 0.4 100 66 0.91 4.1 0.5 220 30 2 10 0.9 330 21 2.86 14 1.1 470 16 3.75 24 2.2 © Sarah Don, Australia, 2008

Analysis and Discussion:

Time (seconds)

Graph 5 - Charge Time of Capacitors 26 24 22 20 18 16 14 12 10 8 6 4 2 0

Charge Discharge

0

50

100

150

200

250

300

350

400

450

500

Capacitance

No. Flashes per Minute

With each value of capacitance tested in the simple circuit on Crocodile Physics, the charge and discharge time increased as capacitance increased, as shown in graph 5. Because of the different values of resistance depending on whether the capacitor was charging or discharging, it took a much shorter time for the capacitors to discharge than it did for them to charge. As shown in diagram 3, while charging, there was 10kΩ Graph 6 - Flashes per minute resistance in the circuit however while discharging, the resistance was much 150 less at only 100Ω. Less resistance resulted in a higher current and therefore 100 a faster discharge. 50 0 0

100

200

300

400

500

Capacitance

1/No. Flashes per Minute

Graph 7 - Frequency of Flashes 0.08 0.06 0.04 0.02 0 0

100

200

300

400

500

As the capacitance increased, the number of LED oscillations per minute decreased as shown in graph 6. The shape of graph 6 is representative of an inverse proportionality. The data from graph 6, when plotted with the number of flashes per minute inversed, forms a straight line graph as shown in graph 7. The frequency of flashes is therefore inversely proportional to the capacitance of the capacitor in the timing circuit. 1 ∝ 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑎𝑛𝑐𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑓𝑙𝑎𝑠ℎ𝑒𝑠

Capacitance

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Graph 8 - How charge and discharge time affect the period of LED oscillation 26 24 22 20 Time (seconds)

18 16 14

Charge

12

Discharge

10

Time between flashes

8 6 4 2 0 0

50

100

150

200

250

300

350

400

450

500

Capacitance

The charge and discharge times of the capacitors affected the number of flashes per minute. The capacitors did not have to fully charge before they were able to supply a sufficient voltage to the base of their corresponding transistors. Also, the LEDs were not lit for the entire duration of their oscillation period because their corresponding capacitor would have discharged before the other capacitor had charged to the point where it could supply a potential difference (0.6V) to the base of the other transistor large enough to switch it on.

Figure 9 – Graphing in Crocodile Physics

There were few minor limitations involved in this investigation. Finding the definite point where a capacitor had charged or discharged was subjective. However, since the same person analysed each set of data for the charge and discharge times of the capacitors, the readings were taken from the same point along the curve each time. The most significant limitation – accurately recording charge and discharge times of the capacitors with a stopwatch – was overcome by using computer software instead that could accurately calculate and graph the curves for voltage against time as the capacitor charged and discharged (as

© Sarah Don, Australia, 2008

shown in figure 9). Another limitation that was encountered was that Crocodile Physics did not allow the quantum theory detector to run virtually, the same way that it did in reality (because of the set up of the integrated circuit). This presented problems when trying to measure the charge and discharge times of the capacitors. However this limitation was overcome by creating the simple circuit with the same resistances that the electricity would have experienced had the charge and discharge time data been taken from measurements from the whole circuit working in reality, and not just from the simple circuit in Crocodile Physics. The graph in figure 9 shows how different the charge time was compared to the discharge time for that particular capacitor because of the difference in resistance in the circuit depending on which way the current was flowing. Conclusion: The hypothesis – that as the capacitance of the capacitors increases, the LEDs oscillate slower – was accepted. A mathematical relationship between capacitance and the LED oscillation frequency was conclusive from the results. LED oscillation frequency graphed against capacitance produced a straight line graph when expressed as an inversely proportional relationship. The frequency of the flashing LEDs does not affect the use of the circuit in a practical context. However in a theoretical context, the faster the LEDs oscillate, the closer they represent the behaviour of light particles/waves and the closer the circuit becomes to creating a quantum instance.

Bibliography: Capgo (2007) Resistors, http://www.capgo.com/Resources/Measurement/MeasHome/Resistors/Resistors.html (11/05/08) Crocodile Clips (2006) Crocodile Physics, Computer Software, United States of America, Crocodile Clips Ltd. Dick Smith Electronics (1979) Funway vol.1, McPherson’s Printing Group, Australia. Hewes, J. (2008) Circuit Symbols, http://www.kpsec.freeuk.com/symbol.htm (10/05/08)

© Sarah Don, Australia, 2008