Frontier physics
Bosonic string theory and superstrings
Explore the vibration patterns of a closed string and map each mode to a «particle» in the spectrum. Check the idea that string oscillations generate a mass tower .
Equipment
- 3D model of an oscillating closed string
- Mode-number and Amplitude sliders
- Pause button to freeze the vibration pattern
Procedure
Count the oscillation modes
With «Amplitude» mid-range, sweep «Mode number» from 1 to 6. For each n, count the antinodes around the loop: mode n fits n wavelengths on the ring — a standing-wave pattern like a guitar string, but closed.
Relate modes to particle mass
In string theory each vibration mode is a different particle: higher mode means heavier particle along the Regge tower . Record a «relative mass» ∝ n for each mode and plot the sequence — this is how a single object (the string) generates a whole particle spectrum.
Role of amplitude and energy
Hold «Mode number» fixed and change «Amplitude»: the vibration energy grows with amplitude but the mode structure (the «particle species») does not — amplitude is the excitation strength while the mode number defines the particle identity. Press «Pause» to capture waveforms and compare different n.
Predict limiting modes and stability
Predict the waveform for n = 6 then verify; note that a closed string admits only integer modes — the closed-loop standing-wave condition. Relate: in superstrings, quantum constraints (Virasoro) remove many «ghost» modes and leave only a physical spectrum — which is why the dimension is fixed (10 for superstrings).