[ Long ] A Philosophy of Science v. Pseudo-Science

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What variables?



Depends on what exactly you mean by mass. If you mean rest mass, it doesn’t depend on the speed of the proton relative to anything. If you mean relativistic mass (though I think this concept is currently being abandoned to reduce confusion, as it’s enough to talk about the total energy of the particle), it’s given by

m′ = E / c² = m / √(1 - v² / c²),

where m′ is the relativistic mass of the particle, E is its energy (sum of rest energy and kinetic energy), v is its speed, all three with respect to a certain reference frame, and m is its rest mass.

If a particle has no energy (or no relativistic mass), there simply is no particle. So, for the quotient

m / √(1 - v² / c²)

not to vanish as m approaches zero (the case of a photon), v needs to approach c. Any speed other than the speed of light causes a particle with zero rest mass to have zero energy, so photons can only exist travelling at the speed of light relative to any reference frame.

Did you miss the part where Fnord and DentArthurDent sorta, um, did, before the quoted was posted?

There was one certain twit on the Internet who claimed to be the world's foremost neuroscientist, mathematician, and physicist.

He showed himself to be bogus pretty soon after I first saw something from him when he referred to the neurofibrillary tangles of those who suffer from Alzheimer's to be tangles of neurons. Any world's foremost neuroscientist would know that neurofibrillary tangles are tangles of very fine structures within neurons, not of neurons themselves.

The more he posted, the crazier he got. He couldn't understand why nobody paid any attention to him.

Choose your units carefully so that c=1 and then you have E=m for a mass at rest. For a mass in motion, it becomes E^2=m^2+p^2 where p is its momentum.

One of the crazies that I've encountered insists that the ratio of the circumference of any given circle to its diameter has been slowly increasing since the world was created in 4004 BCE, and that it will eventually equal 4.004; thus proving that the "Heavans and the Earth" we're created by God, and also signifying that the Final Days have come.

I love it. We should send him a "4004 aniversary card each year".

Years ago I went to work for an engineering company in Houston. The guy I replaced was a member of some church where the preacher predicted the end of the world to be some specific day back then, I think in September or October of 1979.

When the end of the world came and went without any notable changes, the preacher recalculated and found that he was a year off and it was the same day but a year later.

One Monday morning a few months before the revised end of the world, his boss called him in and asked about the date of the end of the world which the guy confirmed. His boss then said that he had just bought a sailboat and scheduled the payments to start after that date so that he would never have to make any payments on the sailboat. He told the guy that if he did have to make any payments because the world didn't end on that date, he was going to blame him for it.

The guy got mad and quit and so I was hired to replace him.

That isn't true, unless mass is equal to 0 (in which case it just becomes E = 0 due to all of the units cancelling out due to the zero*), because m would have the unit only for mass, and E would still have the unit for mass times the unit for speed squared.

So let's make up a speed unit, so that c = 1. I don't know of any speed units that cause c = 1, so we need to make it up. Let's call it q. Then that would cause c = 1 q. Let's use the good old kg for mass. Let us say that m = 100 kg. So plugging into the equation:

E = (100 kg)(1 q)^2

E = (100 kg)(1 q^2)

E = 100 kg x q^2

Notice how E is equal to 100 kg times q squared, but m is just equal to 100 kg, so E and m are NOT equal.

*The only exception for this is a unit in degrees, in which case 0 degrees does not cancel out. Notice how Fahrenheit and Celsius are in degrees, because there are valid temperatures in those units that drop into the negative, but Kelvin is not in degrees, because 0 K (or just 0) constitutes the very lowest temperature anything in the universe may theoretically have (i.e. no negatives are valid).

<* Heavy Sigh *>

Mass–energy equivalence means only that the mass of an object or system is a measure of its energy content.

Thus,


E / m = c^2 = (299,792,458 m/s)^2 = 89,875,517,873,681,764 J/kg (≈ 9.0 × 10^16 joules per kilogram).

So the energy equivalent 'E' of one gram (1/1000 of a kilogram) of mass 'm' is equivalent to:

89.9 terajoules
25.0 million kilowatt-hours (≈ 25 GW·h)
21.5 billion kilocalories (≈ 21 Tcal)
85.2 billion BTUs

or to the energy released by combustion of the following:

21.5 kilotons of TNT-equivalent energy (≈ 21 kt)
568,000 US gallons of automotive gasoline

For instance, the atomic bomb used on Nagasaki had an explosive yield equivalent to 21 kt of TNT. About 1 kg of the approximately 6.15 kg of plutonium in each of these bombs fissioned into lighter elements totaling almost exactly one gram less, after cooling. The electromagnetic radiation and kinetic energy (thermal and blast energy) released in this explosion carried the missing one gram of mass. This occurs because nuclear binding energy is released whenever elements with more than 62 nucleons fission.

Class dismissed.

I assume that you are objecting to the use of geometrized units. In General Relativity, it is quite common to see papers and books that use geometrized units. To say that it is wrong is to say that General Relativity is wrong.

For what it's worth, I don't remember seeing much in Gravitation by Charles Misner, Kip Thorne, and John Wheeler that wasn't in geometrized units, but it's been about 35 years since I took a course with that as the textbook.

So I just now took my copy off of the shelf and looking through it at random, about the only place where I didn't see geometrized units was in the exercise in Box 2.2 on page 54:

The authors then provide two solutions to the exercise, both in geometrized units.

In my graduate class on the subject, I remember the prof mentioning geometrized units, but maybe in a sentence or two. From that point on, we used geometrized units as well.

It’s not really a matter of choosing units, but of establishing an equivalence between length and time.

We usually consider length and time to be two different, independent physical magnitudes, so we give them two different base units, like the metre and the second. However, time is just a particular direction in spacetime, so there’s no problem in measuring lengths along it with the same unit you use for spatial directions. To implement this, you need to impose a certain conversion relation between your units of length and time, so length can be measured in units of time and vice-versa.

On the other hand, if length and time have the same physical dimensions, speed, being length divided by time, becomes a dimensionless magnitude; therefore, the above-mentioned conversion relation can be established more cleanly by agreeing that a certain speed equals the dimensionless quantity 1, i.e., the bare number 1. The obvious choice for this speed within relativity is c, the speed of light. If c = 1 (just 1, no measurement unit), m c² = m.

The reason temperature is measured in such an odd way is that, in everyday life, the existence of an absolute zero is neither readily apparent, nor significant, so people began to measure temperature long before such a limit was discovered. The key isn’t really the word degree—note how angles do have a definitely meaningful zero, and a meaningful addition whose identity element is indeed the zero angle, equal to zero degrees.



In fact, some simple thermodynamic systems can have negative absolute temperatures; however, that doesn’t mean “colder than absolute zero”, but “hotter than infinite temperature”. They can never be in thermal equilibrium with ordinary systems and will always lose heat to them till their temperature reaches a positive value, going through infinity in the process and never passing through zero.

That's a good explanation.

It also simplifies the metric ds^2=-dt^2+dx^2+dy^2+dz^2 since t is inseparable from x, y, and z.

I'm definitely getting too old. Looking at my notes I made in MTW's Gravitation, I have little or no idea what I meant when I wrote them. 35 years ago, they made perfect sense.

^ ^ Thanks both of you this has really cleared up my understanding of the issue. Really wonderful explanation Spiderpig

On the subject of using the same units for distance and time, Grace Hopper used to hand out nanoseconds. Click on the link below to see Grace Hopper give David Letterman a nanosecond.

http://www.youtube.com/watch?v=1-vcErOPofQ

I used to know someone who was given a nanosecond by Grace Hopper. He was pretty proud of that nanosecond.