If you look at the famous equation of Einstein E=MC2, one thing that I noticed, the other day, is, in physics, mass or M is invariant or is the same in all references, while the speed of light C, is also an invariant and is the same in all references. However, energy is variant can vary between references red and blue shift. The questions is, how can the product of two invariant variables (M,C) equal a variable that is variant (E)? This is like saying the product of two constants, equals a nonlinear function?
Mass isn't invariant. Einstein used the difference in mass between reference frames as part of his original derivation.
Yes. For general readers, this (by wellwisher) seems to embody the potential confusion between rest mass and relativistic mass that we ended up discussing at some length in an earlier thread, here:http://www.sciforums.com/threads/about-effective-relativistic-mass-of-photon.156719/ As I understand it, E=mc² is true in any reference frame if by "m" one means the so-called relativistic mass, which is not invariant (gets larger the greater the relative motion between observer and object observed). However nowadays, "m" is generally taken to mean the rest mass, formerly - and still sometimes, for the avoidance of doubt - given the symbol m₀. This is indeed invariant. But, in terms of rest mass, E=mc² is only true when the observer is at rest with respect to the object observed, and for the general case where there is relative motion, the correct expression is a squared up version, involving momentum (p), as follows: E² = m₀²c⁴ + p²c². More here: https://en.wikipedia.org/wiki/Energy–momentum_relation
If I was to convert a Kg of rest mass to pure energy, the equation E=Mc2 will apply. The equation was originally used to calculate the energy output from atomic bombs. If I was on a moving reference, watching the conversion of the 1Kg of rest mass into pure energy, the rest mass will not change and the speed of light does not change. However, the energy output might appear to change from calculated, due to blue to red shift, adding or taking away energy from the product of two invariants. The invariant rest mass, has a specific energy value, defined by E=MC2 that is universal, since the rest mass is invariant. One Kg of rest has a specific energy equivalence value. Energy, however, is not invariant, therefore the choice of reference can cause what should be an invariant amount of energy from 1 kg of rest mass, to appear to depart from the invariant amount. The universal energy balance does not change, because I look at it a certain way tor because I am riding in a rocket near C. That is all ego-centric; I am the center of the universe. Rather there is a reference affect, caused by the variance of energy, than can fool me to mischaracterize the amount of invariant energy, defined by E=Mc2, where M is rest mass. Relativity appears to be about filters of the mind, and what we will see, due to the variance of energy, based on reference. But what we see is not always what exists, based on the universal invariants. One needs to look beyond the surface illusion.
What is it about the equation E² = m₀²c⁴ + p²c² did you not get? Any of it? How can a rocket go near capacitance? What does that even mean?
At least Wellwisher is trying to think about the conceptual basis of relativistic physics. I respect those who do that, even if mistakes are made. Exchemist's post #7 is pretty good, albeit extremely cryptic for those without university-level exposure to physics. But isn't it implicitly agreeing with Wellwisher's original point? The sorta-familiar 'E = MC2' (it's a cultural icon, even though most of us don't have a clue what it means) is problematic on its face and appears to need some modification if it is going to apply to masses in relative motion.
How depressing: I was trying to make it as clear as I could. It isn't agreeing with wellwisher's point because - as I was trying to point out - he was comparing apples with oranges. The conflict wellwisher imagines is that two invariant quantities result in a quantity that is not invariant. This does not arise. You have two ways of looking at it:- i) If you use the invariant mass, which is the rest mass, then E=mc² does not apply when there is relative motion because you have to use the energy-momentum relation instead. The presence of the momentum term, which is relative motion dependent, is what results in the total energy not being invariant. ii) If, on the other hand, you use relativistic mass, then E=mc² does apply in the case of relative motion, but then relativistic mass is not invariant. So again there is no conflict. To your observation about the "iconic" nature of the equation, in popular understanding E=mc² is what people know and think is universally applicable. This goes along, in popular understanding, with the notion of mass increasing as relative motion increases. We've all read, or seen TV explanations in such terms. This is all fine: all it means is that popular understanding is tacitly using relativistic mass. But modern physicists (I understand) rather tend to cringe about this: they tend to deal with rest mass all the time, precisely to avoid the sort of tangle that wellwisher has got into by mixing his definitions.
Our brains can process energy, directly. We can see photons of visible light, which are a part of the EM spectrum. But we have no sensory system for seeing or sensing mass, directly. We need to infer the amount of mass, rest or relativistic, using tools and our visual sensory system, which makes use of energy; look at the scale, displacement or motion. Even though rest mass is defined as an invariant; same in all references, we need to determine that invariant using our sight, which is wired to process energy signals, which have variance due to reference. The paradox of E=MC2, is not in the physical universe, but is connected to the variant of the observational reference, imposed by the human brain's use of energy to observe. Theoretically, there is X amount of rest mass in the universe, that will be the same in all references. The speed of light is also the same in all references. However, observing mass requires we use energy/sight, which are impacted by our frame of references. The practical limitations of the human brain can make a fixed amount of mass appear variant. Einstein came up with a fudge factor to take into account the variance of energy based sight; relativistic mass. Relativity mass is a variant because it is based on the limits of the brain, not on a universal energy balance. If we have two references, moving at relative speed V, one reference has M rest mass and other reference has 2M rest mass, each will see a different relativistic mass, if each assumes the other is in motion. This is because each is using sight, which processes the variant, energy. One can't do a real universal energy balance with sight; direct observation, because the above shows this can lead reference dependent amounts of relativistic mass, for a fixed amount of rest mass, that was propelled with a fixed amount of energy. What we see, is not what it is, but only what it appears to be. Sight makes the earth the center of the universe; chosen relative reference. This is not the same as the invariant universe of rest mass and the speed of light.
We see by virtue of our eyes, which receive some of the spectrum and not all parts in the same way, then our brain interprets the signal from our eyes. That is a long, long way from directly processing energy, especially given all the evidence we have of the flawed nature of human visual processing. And we're back to Christian evangelism.
You apparently did not understand the explanations that were given to you to help clear up your confusion. Too bad, well at least the members tried. Why is this in the philosophy section?
Say humans decided to use the sense of smell, instead of sense of sight, to observe the universe. In this example, one reference has a bakery, while other reference is that of a little boy. The smell is not relative to reference, but is directly connected to the source. The bakery will always have the strongest center of smell/fragrance, no matter the relative motion, because with smell we are dealing with substance, and not with energy. We can determine motional direction and speed of the bakery by noting the change in the directional concentration of the smell. Unlike sight, we can't pretend to be the center of fragrance, because both you and the bakery are in relative motion. Rest mass and the speed of light are like fragrances coming from the muffins and croissants cooling in the universal bakery. You need a different sense, beyond visual, to smell it.
Answer - astronomy would not get very far.Please Register or Log in to view the hidden image! What does Sirius smell like.Please Register or Log in to view the hidden image!
The explanation everyone offered are all limited to the variance imposed by sight. I understood the traditional explanation 30 years ago. But there was something not kosher, which has to do with the limitations of the brain's wiring. Knowing how the brain and consciousness work solved that problem. There is no law in science that requires calibration of the mind, even though this is the key tool.
