What does the Lorentz factor actually mean?

In summary: The idea that clocks do not record some universal time but that each one records the proper time along its own worldline is probably the most counter-intuitive concept ever introduced in physics and was met with a lot of resistance when first mooted. As for the 'real meaning', that mathematical definition is it.In summary, the Lorentz factor is a conversion factor between different measures of duration, length, etc. according to different inertial reference systems.
  • #36
phyti said:
If the path is extended, it will not show anything new. Gamma is still the ratio c/s or (A time)/(U time).
Exactly and that's because the ratio between ct and st is the same for all t. You just have a different size triangle involving ct, st and vt. I just don't know why you think there is anything significant for the specific value of t corresponding to when the photons hit U's mirror. If you had used the value of t corresponding to when the photons hit A's mirror, then st will be equal to r, the distance to U's mirror from O, and ct would be the distance to A's mirror from O, and ct/st = c/s = gamma. If you would draw that diagram, which is the diagram that everyone else draws, then it seems like it would be more helpful to those new to SR.
 
<h2> What is the Lorentz factor?</h2><p>The Lorentz factor, also known as the Lorentz boost factor, is a mathematical term used in special relativity to describe the relationship between an object's relative velocity and its observed time, length, and mass. It is denoted by the symbol γ (gamma) and is defined as γ = 1/√(1-v²/c²), where v is the relative velocity and c is the speed of light.</p><h2> How is the Lorentz factor related to time dilation?</h2><p>The Lorentz factor is directly related to time dilation, which is the phenomenon where time appears to pass slower for objects moving at high speeds. The higher the Lorentz factor, the greater the time dilation. This means that as an object's velocity approaches the speed of light, its Lorentz factor increases and time appears to slow down for that object.</p><h2> What does a Lorentz factor of 1 mean?</h2><p>A Lorentz factor of 1 means that an object is not moving at all, or is moving at a speed much lower than the speed of light. In this case, the Lorentz factor has no effect on the object's observed time, length, or mass. This is known as the rest frame, where an object's measurements are the same in all reference frames.</p><h2> How does the Lorentz factor affect an object's length?</h2><p>The Lorentz factor also affects an object's length, causing it to appear shorter in the direction of motion. This is known as length contraction and is a result of the time dilation effect. As an object's velocity increases, its Lorentz factor increases, causing its length to contract in the direction of motion.</p><h2> Can the Lorentz factor be greater than 1?</h2><p>Yes, the Lorentz factor can be greater than 1. In fact, as an object's velocity approaches the speed of light, its Lorentz factor approaches infinity. This means that an object's observed time, length, and mass will also approach infinity, making it impossible to reach the speed of light. This is known as the speed of light barrier, and it is a fundamental concept in special relativity.</p>

FAQ: What does the Lorentz factor actually mean?

What is the Lorentz factor?

The Lorentz factor, also known as the Lorentz boost factor, is a mathematical term used in special relativity to describe the relationship between an object's relative velocity and its observed time, length, and mass. It is denoted by the symbol γ (gamma) and is defined as γ = 1/√(1-v²/c²), where v is the relative velocity and c is the speed of light.

How is the Lorentz factor related to time dilation?

The Lorentz factor is directly related to time dilation, which is the phenomenon where time appears to pass slower for objects moving at high speeds. The higher the Lorentz factor, the greater the time dilation. This means that as an object's velocity approaches the speed of light, its Lorentz factor increases and time appears to slow down for that object.

What does a Lorentz factor of 1 mean?

A Lorentz factor of 1 means that an object is not moving at all, or is moving at a speed much lower than the speed of light. In this case, the Lorentz factor has no effect on the object's observed time, length, or mass. This is known as the rest frame, where an object's measurements are the same in all reference frames.

How does the Lorentz factor affect an object's length?

The Lorentz factor also affects an object's length, causing it to appear shorter in the direction of motion. This is known as length contraction and is a result of the time dilation effect. As an object's velocity increases, its Lorentz factor increases, causing its length to contract in the direction of motion.

Can the Lorentz factor be greater than 1?

Yes, the Lorentz factor can be greater than 1. In fact, as an object's velocity approaches the speed of light, its Lorentz factor approaches infinity. This means that an object's observed time, length, and mass will also approach infinity, making it impossible to reach the speed of light. This is known as the speed of light barrier, and it is a fundamental concept in special relativity.

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