Prove Lorentz Factor w/o Speed of Light

In summary, the Lorentz factor is a mathematical concept that takes into account the relative motion between two frames and shows how one frame will judge speeds in another frame. The speed of light is used in the Lorentz factor, but it is not necessarily fundamental to it. There are various ways to derive the Lorentz transform, but they all require equations and mathematics. The Pal paper is a good resource for understanding the differences between Galilean relativity and Einsteinian relativity in relation to the speed of light. Even if it is discovered that the speed of light is not constant, the theory of relativity will still hold.
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The Lorentz factor shows how fast one frame will judge speeds in another frame to be taking into account the relative motion between the two frames.

The speed of light is a factor in the Lorentz factor but I have heard that this is not because the speed of light is fundamental to it.

So how can this result be attained from first principles and without involving the speed of light as such?
 
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  • #2
geordief said:
...but I have heard that this is not because the speed of light is fundamental to it.
You will get better and more helpful answers if you can tell us exactly what you heard and where you heard it.
 
  • #3
Thanks. I can't remember.

Do you think I may have misheard?

Even so am fairly confident that I have heard more than once that it is not the speed of light that is responsible for the Lorentz factor (as stated by Einstein).

That being so I wonder why it is such a factor in the transformations -and ,as I say can this result be got without recourse to a scenario involving the transmission of a light signal between the two frames ?
 
  • #4
geordief said:
So how can this result be attained from first principles and without involving the speed of light as such?
There are many ways to derive this result, but I don't know of any that work at a B-level, they all require equations of varying degrees of difficulty. If you have the stomach for mathematics, this is my favorite derivation of the Lorentz transform.
 
  • #5
m4r35n357 said:
There are many ways to derive this result, but I don't know of any that work at a B-level, they all require equations of varying degrees of difficulty. If you have the stomach for mathematics, this is my favorite derivation of the Lorentz transform.
thanks,that looks interesting. At a quick glance over I see c is introduced as some kind of an unspecified scaling factor without reference to light.

It will take me a good while to go through it but it seems very helpful.
 
  • #6
Pal's paper is also good.
https://arxiv.org/abs/physics/0302045

He starts with the principle of relativity and shows that there are two options: Galilean relativity (with an infinite invariant speed), or Einsteinian relativity (with a finite invariant speed). Checking which transform holds in the real world may be done by experiment (e.g. Bertozzi's experiment measuring the relation between velocity and kinetic energy of electrons). And then we merely note that the implied value of the invariant speed is c.
 
  • #7
Ibix said:
Pal's paper is also good.
https://arxiv.org/abs/physics/0302045

He starts with the principle of relativity and shows that there are two options: Galilean relativity (with an infinite invariant speed), or Einsteinian relativity (with a finite invariant speed). Checking which transform holds in the real world may be done by experiment (e.g. Bertozzi's experiment measuring the relation between velocity and kinetic energy of electrons). And then we merely note that the implied value of the invariant speed is c.
thanks, I will take a look at that too.
 
  • #8
Ibix said:
Pal's paper is also good.
https://arxiv.org/abs/physics/0302045

He starts with the principle of relativity and shows that there are two options: Galilean relativity (with an infinite invariant speed), or Einsteinian relativity (with a finite invariant speed). Checking which transform holds in the real world may be done by experiment (e.g. Bertozzi's experiment measuring the relation between velocity and kinetic energy of electrons). And then we merely note that the implied value of the invariant speed is c.
It is also nice in that it emphasises that Galilean relativity and Einstein's relativity only differ in one single aspect: the speed of light.

Both relativity theories say that inertial observers are equivalent, and they all measure the same speed of light. In Galilean relativity, this speed is infinite.
 
  • #9
haushofer said:
It is also nice in that it emphasises that Galilean relativity and Einstein's relativity only differ in one single aspect: the speed of light.
As does the Reflections on Relativity one.
 
  • #10
geordief said:
thanks,that looks interesting. At a quick glance over I see c is introduced as some kind of an unspecified scaling factor without reference to light.

This is perhaps related to your original question. If it's discovered that the speed of light depends on the relative motion of the observer or source, then nothing about the theory will change. In a relation like ##\gamma=\frac{1}{\sqrt{1-(v/c)^2}}## we will simply stop referring to ##c## as the speed of light and call it something else. Like the invariant speed, or the ultimate speed. Nothing about the theory will change.

The theory describes an invariant speed ##c## even if light or indeed anything at all, never travels at that speed.
 
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What is the Lorentz Factor and why is it important in physics?

The Lorentz Factor, denoted by the symbol γ, is a term used in special relativity to describe the relationship between an object's velocity and its mass, length, and time. It is important because it helps us understand the effects of time dilation, length contraction, and mass increase at relativistic speeds.

Can the Lorentz Factor be derived without using the speed of light?

Yes, the Lorentz Factor can be derived without using the speed of light. It can be derived from the equations of special relativity, which are based on the assumption that the laws of physics are the same in all inertial reference frames.

How is the Lorentz Factor calculated?

The Lorentz Factor can be calculated using the formula γ = 1 / √(1 - v2/c2), where v is the velocity of the object and c is the speed of light. This formula takes into account the effects of time dilation, length contraction, and mass increase at relativistic speeds.

What are the implications of a high or low Lorentz Factor?

A high Lorentz Factor, meaning an object is moving at relativistic speeds, has significant implications in physics. It can lead to time dilation, where time appears to slow down for the moving object, and length contraction, where the length of the object appears to decrease in the direction of motion. A low Lorentz Factor, on the other hand, indicates that an object is moving at non-relativistic speeds and the effects of special relativity are negligible.

Can the Lorentz Factor be used in other areas of science?

Yes, the Lorentz Factor is not limited to just physics. It is also used in other areas of science, such as astrophysics and cosmology, to understand the behavior of objects moving at high speeds, such as stars and galaxies. It is also used in engineering, particularly in the design of particle accelerators and spacecraft, where the effects of special relativity must be taken into account.

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