Can Two Different Physical Theories Yield the Same Predictions?

In summary, "Equivalent theories exist" means that there can be multiple theories that are equally valid and can produce the same results for a particular phenomenon. These theories can have different assumptions or principles but are still considered equivalent. Scientists determine if two theories are equivalent by comparing their predictions and results. While equivalent theories are equally valid, they may not always be interchangeable due to different practical applications or methods.
  • #1
Robin04
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Is it possible that two physical theories are equivalent in the sense that their predictions are exactly the same but the mathematics they use is different?
 
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  • #2
Like Newtonian and Lagrangian mechanics?
 
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Vanadium 50 said:
Like Newtonian and Lagrangian mechanics?

Yes, exactly, thank you! Are there any modern examples? Are physicist trying to reconstruct some theories in this way?
 

1. What does it mean when someone says "equivalent theories exist"?

When someone says "equivalent theories exist," they are referring to the idea that there can be multiple different theories or explanations for a particular phenomenon that are equally valid and can produce the same results.

2. Can two theories be considered equivalent if they have different assumptions or principles?

Yes, two theories can still be considered equivalent even if they have different assumptions or principles. As long as they can produce the same results and explain the same phenomenon, they can be considered equivalent.

3. How do scientists determine if two theories are equivalent?

Scientists determine if two theories are equivalent by comparing their predictions and results. If they both produce the same results and can explain the same phenomenon, they can be considered equivalent.

4. Are equivalent theories equally valid?

Yes, equivalent theories are equally valid. They may have different assumptions or principles, but as long as they can explain the same phenomenon and produce the same results, they are both considered valid explanations.

5. Can equivalent theories be used interchangeably?

Not necessarily. While equivalent theories are equally valid, they may have different practical applications or use different methods to achieve the same results. Therefore, they may not always be interchangeable in a specific context or situation.

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