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I'm really confused about invariant quantities.Could someone explain which quantities are invariant in special relativity and how are they recognised?
thanks
thanks
ghwellsjr said:If you measure a ball to be moving at velocity v then it is a proper invariant measurement and every frame of reference can show that you will get the value v when you make that measurement.
We agree that you will measure a velocity v and that I will measure a velocity u and we agree that the ball measures its own velocity to be 0. So we each agree on the result of any given measurement. What we do not agree on is whether or not the thing that the other people measured represents the ball's velocity. Similarly with any frame variant quantity like position, length, duration, energy, momentum, etc.Shyan said:thanks.good explanations.I got it.
But it seems velocity is different.
imagine In my frame of reference,a ball is moving with the velocity v.But at yours its u.what should we agree on?the one which is measured in the ball's frame and that's 0.so what?
I'm wondering is there anything else?
Well looks like if we just stick to a proper frame we won't have to deal with such problems.
yeah I understood.
thanks a lot
When you measure the velocity of a ball, you do not have to establish or reference any reference frame to make your measurements. You just measure it by any means at your disposal. If you or anybody else observes you making that measurement, they will agree that you have made the correct measurements using your instruments and made the correct calculation to arrive at your correct assessment of the velocity, even if they cannot see the values on your measuring devices. They can see what you will measure because they will see that your rulers are length contracted and they will see that your clocks are time dilated and they can independently verify that your measurements are correct. This, of course, assumes that the ball is not accelerating in which case the problem is in a different ballpark.jtbell said:I've added boldface to a word that I consider to be key in the following statement.
To elaborate on this, suppose that you measure the velocity of the ball (in your reference frame) using a device that has a digital display of the measured velocity. If it reads "5.00 m/s," then everybody who looks at your device, regardless of whether they are moving relative to you or not, will agree that the device reads "5.00 m/s".
The concept of invariant quantities in special relativity refers to physical quantities that remain unchanged regardless of the observer's frame of reference. These quantities include the speed of light, space-time interval, and mass-energy equivalence.
Invariant quantities are central to the theory of special relativity as they help explain the laws of physics in a consistent manner for all observers, regardless of their relative motion. The constancy of these quantities is a fundamental principle of special relativity.
One example of an invariant quantity in special relativity is the speed of light. According to Einstein's theory, the speed of light in a vacuum is the same for all observers, regardless of their relative motion. This is true even if the observers are moving at different speeds or in different directions.
Invariant quantities differ from other physical quantities in that they are not affected by an observer's frame of reference. Other physical quantities, such as velocity and time, can vary depending on the observer's perspective, but invariant quantities remain constant.
Invariant quantities are important in special relativity because they help us understand how the laws of physics behave in different frames of reference. By using these quantities, we can make accurate predictions and calculations that are consistent for all observers, allowing us to better understand the nature of space and time.