Originally posted by amolv06I think you just have to derive the Lorentz transformation formulae. Haven't actually done that myself so I don't know how difficult that is.
This is probably something I would have to work out. I've never actually seen the derivation for relativistic mass -- it was only presented as an experimental fact. I've heard it can be done, though. I'll look into it, and perhaps make a post about it some time.
Originally posted by KazetNagorraThe only way I know how to derive the lorentz transformation is through a thought experiment. This derivation, though, only works for the space and time transformation. In class, the concept of relativistic mass was presented as an experimental fact that allows the conservation of momentum law to hold at relativistic velocities. If there is any interest, though, I could do the space and time transformation. Let me know if you're interested.
I think you just have to derive the Lorentz transformation formulae. Haven't actually done that myself so I don't know how difficult that is.
Originally posted by amolv06Though I do understand that c^2 can be considered a conversion factor if you see the equation as showing that mass is energy and thus that it is merely an equation for converting the two.
I have derived Einstein's formula, and stated my case for why c^2 should be considered a conversion factor on my newly started blog.
However, I still object to the claim that it is merely a conversion factor. It is, in fact, much more. It tells us that the relationship between energy and mass is directly related to the speed of light. Further, it even allows us to derive the speed of light without actually doing a direct measurement. And lastly, it tells us that if the speed of light is not constant, then the mass - energy equivalence is no-longer an equivalence, which could have interesting consequences for the laws regarding conservation of energy.
In other words, I object to your claim "In Einstein's famous equation, this is the purpose of the speed of light factor." Who gets to decide what the "purpose" of an equation is, and why?
Does the famous formula of Einstein really say that the speed of light is a constant? I don't think so.
It says that if you convert matter to energy you get a different amount if it is in an area of universe or an era in time where the velocity of light is different.
However, I do believe that the velocity of light really is a constant, but the equation doesn't say so.
Correct me if I'm wrong, but I disagree with the statement that E=mc^2 says nothing about the constancy of the speed of light. While nothing explicitly states that the speed of light is constant, I believe it is implicit in the equation, as it was derived based off of this assumption. If light speed is not constant, then this violates one of the postulates of special relativity, and that equation is rendered meaningless. So if one is to accept Einstein's formula, one must implicitly accept the constancy of light-speed.
Originally posted by amolv06E=mc^2 is derived with the assumption that the speed of light is constant, so saying that E=mc^2 implies that c is constant is logically wrong (affirmation of the consequent).
Correct me if I'm wrong, but I disagree with the statement that E=mc^2 says nothing about the constancy of the speed of light.
In the context of theory I think that the former is quite easy to understand: you don't prove a thing that you assumed in the beginning. Take this example:
I assume that chickens are blue.
If I have teeth than chickens are blue.
I have teeth, so chickens are blue.
The problem with that syllogism is that my conclusion is assumed in my premises. If you were to conclude that E=mc^2 implies that c is constant you'd be incurring in the same mistake.
Now for the experimental part:
We assume that c is constant. We derive E=mc^2. We go to laboratory and in all experiences that we get to measure we see that E=mc^2 holds up.
By assuming that c is constant we derived E=mc^2 and this formula hold his own in the lab. Does this experimental evidence allows us to conclude that c indeed is constant?
The answer is no. "Why?" some may ask. Forgetting about other assumptions during the derivation of E=mc^2 all that we did was just an implication relationship. The constancy of c and the universality of the laws of physics for inertial observers implies that E=mc^2. And if we by checking out experimentally that E=mc^2 indeed holds up we'd conclude that c is constant we'd be falling for the fallacy of the affirmation of the consequent.
As an example:
Imagine that you're waiting for Pierre and you don't know him. The only thing that you know about him is that he speaks french.
In the language of an implication: If ti is Pierre than he speaks french.
It is Pierre -> speaks french.
So if someone went to talk with you and spoke in french waht would you conclude? You couldn't conclude a thing because we never stated that Pierre is the only french speaking human.
Since we never proved that only by assuming that c is constant we can arrive at E=mc^2 we also can't conclude that E=mc^2 implies the constancy of c.
Originally posted by amolv06You are not wrong in disagreeing ... You have every right in this.
Correct me if I'm wrong, but I disagree with the statement that E=mc^2 says nothing about the constancy of the speed of light. While nothing explicitly states that the speed of light is constant, I believe it is implicit in the equation, as it was derived based off of this assumption. If light speed is not constant, then this violates one of the postulates ...[text shortened]... one is to accept Einstein's formula, one must implicitly accept the constancy of light-speed.
I think that the speed of light is the same all over the whole universe, no matter where and when. But I don't think E=mc2 says so. I can easily think that in a sister universe the light of speed is differently, and E=mc2 still holds there.
Scientists are still measuring speed of light in different scenarios to show that the universal 'constants' has changed since BigBang. The equations show their constance, but they still looking for their variability.
We assume that the speed of light is a constant. A very good assumption.
Sure, we don't know if the speed of light is constant. And I suppose in a hypothetical universe where the speed of light is variable one may incidentally arrive at the same equation. But the equation from our universe, and the equation from the hypothetical universe would have to be arrived at in a very different manner. In our universe, the equation was arrived at based on the assumptions of special relativity. For it to hold, the velocity of light must be constant. This is the domain it operates under. If it is found that the "constants" of nature have changed through space or time, the equation would have to be revised. But, for now, I think e=mc^2 certainly does say that the speed of light is constant. All you have to do is run the derivation in reverse. Then, when you finally come to the end of it, you will see that "oh, yea... I guess this works when the speed of light is constant." Again, someone correct me if I'm wrong.
Originally posted by amolv06Well, historically, the Lorentz transformations were derived in electrodynamics because those are the equations under which transformations are invariant in Maxwell's equations. Initially people wanted to "fix" electrodynamics (despite the "elegance" of Maxwell's equations) and that's where the aether came in. Einstein realized that there was no need for an aether if mechanics, rather than electrodynamics, was accomated to work with the same transformations. If you do that, then relativistic mass shows up as well, but these days people normally write E = gamma mc² and only use the rest mass (personally, I think this makes a lot more sense too).
The only way I know how to derive the lorentz transformation is through a thought experiment. This derivation, though, only works for the space and time transformation. In class, the concept of relativistic mass was presented as an experimental fact that allows the conservation of momentum law to hold at relativistic velocities. If there is any interest, though, I could do the space and time transformation. Let me know if you're interested.
Originally posted by amolv06Don't you have some text on special relativity? There's got to be something about the Lorentz transformations in there.
Thanks for the info. I may go ahead and derive the Lorentz transformation anyway through the two postulates of relativity thursday or friday. This will be a good review for me anyway. As for how relativistic mass shows up, I'll have to read up.