Part 1: Hypothesizing a Darker Material
Step 1: Mathematical Representation of Vantablack
Vantablack is known for its extreme light absorption properties, absorbing 99.965% of visible light¹. Let’s denote the light absorption capacity of Vantablack as AVBA_{VB}:
AVB=0.99965A_{VB} = 0.99965
Step 2: Hypothetical Darker Material
To hypothesize a material darker than Vantablack, we need to consider the properties of anti-light. If anti-light repels light and enhances absorption, we can introduce a factor kk to represent this enhancement. Let’s denote the absorption capacity of our new material as ANMA_{NM}:
ANM=k⋅AVBA_{NM} = k \cdot A_{VB}
Step 3: Determining the Enhancement Factor kk
Assuming anti-light properties significantly enhance absorption, we can hypothesize that kk is greater than 1. For instance, if:
k=1.0001k = 1.0001
then the new material would absorb slightly more light than Vantablack. The calculation becomes:
ANM=1.0001⋅0.99965andANM≈0.99975A_{NM} = 1.0001 \cdot 0.99965 \quad \text{and} \quad A_{NM} \approx 0.99975
This means our new material would absorb approximately 99.975% of visible light, making it darker than Vantablack.
Step 4: Practical Application
- Material Design: Using advanced carbon nanotube structures, we can attempt to create a material that incorporates anti-light properties. This might involve arranging the nanotubes in a way that maximizes both light repulsion and absorption.
- Experimental Validation: By measuring the light absorption of the new material and comparing it to Vantablack, we can validate our theoretical calculations.
Conclusion for Part 1
By mathematically representing Vantablack and incorporating our theories on anti-light, we can predict and potentially create a material darker than any currently known. This approach combines theoretical physics with materials science to push the boundaries of what we understand about light and darkness.
Part 2: Theoretical Calculations to Surpass the Current Absorption Limit of 99.995%
Step 1: Current Absorption Limit
The current best materials absorb up to 99.995% of light. Let’s denote this absorption capacity as AcurrentA_{current}:
Acurrent=0.99995A_{current} = 0.99995
Step 2: Introducing Anti-Light Properties
To incorporate anti-light properties, we introduce an enhancement factor kk. This factor represents the additional absorption capacity provided by anti-light properties.
Step 3: Hypothetical Absorption Capacity
Let’s denote the absorption capacity of our new material as AnewA_{new}. We can express this as:
Anew=k⋅AcurrentA_{new} = k \cdot A_{current}
Step 4: Calculating the Enhancement Factor kk
To surpass the current absorption limit, kk must be greater than 1. Let’s hypothesize a reasonable value for kk based on the theoretical enhancement provided by anti-light properties. For instance, if we assume:
k=1.0001,k = 1.0001,
then the calculation is:
Anew=1.0001⋅0.99995A_{new} = 1.0001 \cdot 0.99995
Anew≈0.99995+0.0001⋅0.99995A_{new} \approx 0.99995 + 0.0001 \cdot 0.99995
Anew≈0.99995+0.000099995A_{new} \approx 0.99995 + 0.000099995
Anew≈0.999949995A_{new} \approx 0.999949995
This calculation shows that with k=1.0001k = 1.0001, the new material would absorb approximately 99.9950995% of light, which is slightly better than the current best.
Step 5: Exploring Higher Enhancement Factors
To achieve a more significant improvement, we can explore higher values of kk. For example, if:
k=1.0005,k = 1.0005,
then:
Anew=1.0005⋅0.99995A_{new} = 1.0005 \cdot 0.99995
Anew≈0.99995+0.0005⋅0.99995A_{new} \approx 0.99995 + 0.0005 \cdot 0.99995
Anew≈0.99995+0.000499975A_{new} \approx 0.99995 + 0.000499975
Anew≈0.999949975A_{new} \approx 0.999949975
This results in an absorption capacity of approximately 99.9994975%, which is a significant improvement over the current best.
Final Conclusion for Part 2
By incorporating anti-light properties and using an enhancement factor kk, we can theoretically surpass the current absorption limit of 99.995%. The exact value of kk would depend on the specific properties of the anti-light material and how effectively it can be integrated into the material’s structure.
Notes:
- All numerical values are idealized and based on theoretical assumptions.