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If the short run total product is dropping at the same time that more workers are being hired, then the marginal physical product must also be dropping.
The short run total product of a firm is the amount of product that the firm produces using a given level of fixed inputs. A total product curve typically shows the amount of production compared to the amount of a variable input like labor. It holds things like the amount of machinery constant and looks at the changes in total product when the amount of labor changes.
Marginal physical product is a measure of how the firm’s physical output (as opposed to its revenue) changes when the level of some input changes. Typically, it measures how much each new worker adds to the amount of product that the firm is putting out.
If the total product that the firm makes is declining, then the marginal product must be declining as well. If the total product goes down, it is not possible that each new worker has added to the total product. Therefore, marginal physical product must be negative in this case.
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