Sure - if you own a bond maturing in 10yrs and paying a coupon of 2% yearly, what you have is a series of cash flows of 2 2 2 2 2 ... 102. In other words, a treasury bond can be decomposed into a series of zero coupon cash flows (interest payments+principal re-payment). The price of a 'whole bond' is the sum of the prices of the different zero coupon cash flows.
A bond maturing in 30yrs has at least 10yrs of cash flows that line up with the 10yr bond. Since coupon interest payments can be 'stripped' from one bond and 'reconstituted' in another bond through the federal reserve, the price of matched-maturity zero coupon cash flows, even if they are stripped from different bonds, is the same. If they weren't, there would be an arbitrage opportunity to buy the cash flows of one bond and sell the cash flows of another bond, exchange them at the Fed, and lock in an immediate profit. Sometimes arbitrage opportunities like this do exist, but typically it's due to liquidity events where it becomes impossible finance offsetting positions. There's a good article on this called "Notes on Bonds: Liquidity at all Costs in the Great Recession" by Musto, Nini, and Schwarz
A bond maturing in 30yrs has at least 10yrs of cash flows that line up with the 10yr bond. Since coupon interest payments can be 'stripped' from one bond and 'reconstituted' in another bond through the federal reserve, the price of matched-maturity zero coupon cash flows, even if they are stripped from different bonds, is the same. If they weren't, there would be an arbitrage opportunity to buy the cash flows of one bond and sell the cash flows of another bond, exchange them at the Fed, and lock in an immediate profit. Sometimes arbitrage opportunities like this do exist, but typically it's due to liquidity events where it becomes impossible finance offsetting positions. There's a good article on this called "Notes on Bonds: Liquidity at all Costs in the Great Recession" by Musto, Nini, and Schwarz