Einstein has two theories of relativity- The Special Theory of Relativity (SRT) and The General Theory of Relativity (GRT). Each theory is based on an assumption about light which follows from the mutual employment of two postulates. This assumption states that light, when it travels through empty space, travels at the constant velocity of c with respect to the reference systems (or observers) identified in the first postulate.

Einstein’s second postulate remains the same in each theory but the first postulate is generalized from SRT to GRT via his "Principle of Equivalence". Einstein’s second postulate is called The Principle of the Constancy of the Velocity of Light. In SRT, the first postulate is called The Special Principle of Relativity (SPR). In GRT, the first postulate is called The General Principle of Relativity (GPR).

Einstein introduces his second postulate as a new law of optics. The second postulate says that light travels at the constant velocity of c, when it travels through empty space. The first postulate identifies the reference systems within which the laws of optics (and therefore Einstein’s second postulate) can claim validity.

Einstein does not prove what reference systems the laws of optics can claim validity in right away. Rather, Einstein tells us first what reference systems the laws of mechanics can claim validity in and then, through a magnet and conductor illustration, tells us that, "examples of this sort…lead to the conjecture that… for every reference system in which the laws of mechanics are valid, the laws of electrodynamics and optics are also valid (Einstein’s relativity paper of 1905)".

SPR says that laws of mechanics (and consequentially laws of electrodynamics and optics) remain valid only in the reference systems which do not rotate or accelerate in translation with respect to one another. GPR says that the laws of mechanics (and consequentially the laws of electrodynamics and optics) remain valid in all reference systems.

One might wonder why it is that Einstein didn’t just introduce his assumption about the velocity of light straight away. That is, why did Einstein introduce his postulates in the first place, instead of just introducing the assumption that light travels at the constant velocity of c, when it travels through empty space, with respect to all reference frames and observers? Either way, Einstein introduces an assumption which receives no justification. In his postulates, this assumption is contained in the second postulate. The second postulate is not justified. It is only introduced as a new law of optics. Einstein believed that his assumption about the velocity of light was better justified by introducing it to follow from two postulates, but this author feels that this introduction is nothing other than a more complicated way to introduce his assumption about light.

At any rate, we are here concerned in this paper with Einstein’s postulates. Einstein’s postulates revolve around the idea that it has to be proven as to whether or not a law of physics is valid for an observer or in a reference frame. The reason why Einstein, in 1905, thinks that laws of classical mechanics are only valid in some frames but not in other frames is because he feels that the motion of a test mass which Newton and Galileo referred to was always supposed to be taken with respect to a reference frame (or observer).

The current opinion of today agrees with Einstein that the motion of a test mass referred to by Newton and Galileo is supposed to be taken with respect to a reference frame. As an example, let us say that there are only two masses in the universe. There is the earth and there is a ball. When the ball is near the surface of the earth it will fall at 9.8 m/s/s with respect to the earth. But when the ball is moved to a distance very far away from the earth, it will not accelerate with respect to the earth. Newton’s first law treats this second case. Newton’s first law says that the ball will not accelerate because there are no forces acting on the ball. But "not accelerate" with respect to what? The current opinion of today interprets that Newton meant "not accelerate with respect to a reference frame". It is the opinion of this author that Newton meant "not accelerate with respect to the earth".

So let us describe the acceleration of a ball in a reference frame. The motion of this ball, with respect to the earth, can be described in any reference frame of our choice. The ball will only have no acceleration with respect to a reference frame provided that the reference frame is chosen not to accelerate with respect to the ball (or the earth, since they are not accelerating with respect to one another). Einstein’s opinion, and the current opinion of today, believes that Newton’s first law is violated in a reference frame chosen to accelerate with respect to the ball (and earth), even though, in this reference frame, the ball still does not accelerate with respect to the earth. It is the opinion of this author that Newton’s first law is not violated in reference frames chosen to accelerate with respect to the ball (and earth).

It is the opinion of this author that neither Newton, nor Galileo, nor anybody else who existed before Einstein, interpreted that the motion described in laws of classical physics was supposed to be taken with respect to a reference frame. Rather, it is the opinion of this author that the laws of classical physics only attempt to describe the motion of something in the real physical world with respect to something else in the real physical world. Since Einstein’s postulates rely on an interpretation about laws of physics which opposes the interpretation that this author has about the laws of physics, we will in this paper first look at the laws of classical physics and what reference frames have to do with laws of classical physics.

In general, contrary to the Einsteinian interpretation, and even contrary to the popular opinion of today, laws of classical physics have nothing to do with observers or reference frames. Laws of classical physics only attempt to identify and predict the motion of something in the real physical world (like a test mass, a test charge, or a test light pulse) with respect to something else in the real physical world (like a source mass, a center of mass of a system of test masses, a magnet, a conductor, a source of the light, or an ether). According to classical physics, this relative motion remains independent of the observer who happens to be viewing this relative motion. And according to classical physics, this relative motion can be described in any reference frame we choose to describe this relative motion in. It might be more convenient to describe this relative motion in a particular reference frame (or a particular set of reference frames) but only convenient. This relative motion can be described in any reference frame, no matter how inconvenient we choose for it to be.

Let us consider the laws of classical mechanics. There are four. There are Newton’s three laws of motion and there is Newton’s law of Gravitation. Einstein refers to Newton’s first law as Galileo’s principle.

Laws of classical mechanics say that a ball, if it is dropped or thrown near the surface of the earth, will fall at 9.8 m/s/s with respect to the earth. The ball will fall at 9.8 m/s/s with respect to the earth regardless of whether it is dropped or thrown by a person, and regardless of whether this person happens to be in a vehicle (like a train or a boat) which is traveling on earth at the time. The ball will fall at 9.8 m/s/s with respect to the earth regardless of how the vehicle happens to be moving on earth.

Do Newton’s laws attempt to describe the acceleration of this ball with respect to some observer? NO. Do Newton’s laws attempt to describe the acceleration of this ball with respect to the vehicle that the ball happens to be dropped or thrown in? NO. Do Newton’s laws attempt to describe the acceleration of the ball with respect to some reference frame? NO. Newton’s laws only attempt to describe the acceleration of the ball with respect to the earth. This will always be 9.8 m/s/s, regardless of who is observing, what vehicle the ball is thrown in, or which reference frame we describe the situation in.

This situation can be most conveniently described in a reference frame glued to the earth. This situation can also be conveniently described in a reference frame chosen to travel at a constant velocity with respect to the earth. But it is inconvenient to describe the motion of the ball in a reference frame chosen to accelerate at, say, 5 m/s/s with respect to the earth. Why? Because then the acceleration of the ball with respect to the earth will be different from the acceleration of the ball with respect to our reference frame. In this frame, the acceleration of the ball with respect to the frame would have two components: 9.8 m/s/s and 5 m/s/s. In this frame, the earth would accelerate at 5 m/s/s. Does this mean that Newton’s first law is violated in this frame because the earth is accelerating in this frame and there is no apparent cause of the acceleration? I don’t think so. I don’t think so because Newton’s first law does not say that a test mass (in this case the earth) will not accelerate with respect to a reference frame if no forces are acting on it. Rather, Newton’s first law only says that a test mass will not accelerate with respect to the sources of the forces if there are no forces acting on it. (We assume that these sources are not acted on either. Otherwise, we will be tracing the reference for acceleration to the center of mass of the universe.)

Let us consider now a different example. Let us consider the relative motion between the planets and the sun in our solar system. This relative motion can be most conveniently described in a reference frame glued to the center of mass of our solar system. This relative motion can also be conveniently described in a reference frame chosen to move at a constant velocity with respect to the center of mass of our solar system. But it is inconvenient to describe this situation in a reference frame chosen to accelerate at, say, 10 m/s/s with respect to the center of mass of the solar system. Why? Because in this frame the acceleration of the planets and the sun with respect to the center of mass of our solar system would be different from the acceleration of the planets and the sun with respect to our reference frame. In this frame, the acceleration of the planets and the sun with respect to the frame will have two components. One component is their acceleration with respect to the center of mass of the solar system. The other component is 10 m/s/s. In this frame, the center of mass of the solar system will accelerate at 10 m/s/s with respect to the frame. Does this mean that Newton’s first law has been violated in this frame because the center of mass of the solar system is accelerating with respect to the frame and there is no apparent cause of this acceleration? I don’t think so. I don’t think so because Newton’s first law does not say that the center of mass of the solar system will not accelerate with respect to some reference frame. Rather, Newton’s first law only says that the center of mass of the solar system will not accelerate with respect to other source masses (i.e. like the stars in the sky) if they are far removed and have no influence on the motion of the center of mass of our solar system.

The relative motion of the planets and the sun can in fact be described in the very inconvenient reference frame glued to the earth. Kepler had only this frame to work with. But are Newton’s laws violated in this frame because the center of mass of our solar system rotates and revolves about the origin of our reference frame? I don’t think so. I don’t think so because Newton’s laws make no claims about how the planets and the sun will move in some circumstantial reference frame. Newton’s laws only attempt to describe the motion of the planets and the sun with respect to one another. And this remains the same in a frame glued to the earth as it does in any frame we choose.

There are six laws of classical electrodynamics and they were all enunciated by Maxwell. They are Gauss’ law, the law of no magnetic monopoles, Ampere’s law, Faraday’s law, the conservation of charge equation, and the Lorentz force equation.

Maxwell’s equations offer two alternative explanations for the current circulation which arises in a conductor when a magnet and conductor are moved very slowly with respect to one another on earth. One explanation describes the motion of the current with respect to the magnet. The other explanation describes the motion of the current with respect to the conductor. (It is the opinion of this author that this indicates a redundancy inherent in Maxwell’s equations).

Does either explanation provided by Maxwell attempt to describe the motion of the current with respect to an observer? NO. Does either explanation attempt to describe the motion of the current with respect to a reference frame? NO. One explanation can be most conveniently illustrated in a reference frame glued to the magnet. The other explanation can be most conveniently illustrated in a reference frame glued to the conductor. But either explanation can be used to describe the current circulation in any reference frame of our choice. This is because the relative motion between the current, conductor, magnet and earth can be described in any reference frame we choose to describe it in. And Maxwell’s equations only attempt to describe the relative motion between the magnet, conductor, and the current.

The laws of optics are any and all equations or theories which attempt to describe the velocity of light. And here we are concerned with the velocity of light through empty space. The electromagnetic equation, which is derived from Maxwell’s equations, is such an equation.

Prior to Einstein, there were proposed two theories which attempted to describe what it is that light travels isotropic (same speed in all directions) to, when it travels through empty space. The ballistic theory says that light travels isotropic to some source of the light. The ether theory says that light travels isotropic to some ether.

The ballistic theorists would say that the velocity of light can most conveniently be described in a reference frame glued to the source of the light. The ether theorists would say that the velocity of light can most conveniently be described in a reference frame glued to the ether. The reason why they would say these frames are more convenient than other frames is because, according to their theories, the light would travel isotropic to these frames. In other words, in these frames, the centers of wavefront spheres would not move. These theorists would not be opposed to describing the velocity of light in other frames, but they would just say that it would be inconvenient to do so because then the centers of the wavefront spheres would have to be drawn to move.

Some (stationary) ether theorists went so far as attempting to reformulate the Maxwell’s laws of electrodynamics (which were derived from experiments performed at rest on earth) so that they might be written with respect to the ether (i.e. as opposed to being written with respect to the earth).

Einstein: We’ve been having a lot of trouble trying to detect this ether. And the ballistic theory doesn’t seem to be working out either. So I’d like to offer a new possibility. It is to be a new law of optics. This law says that light, when it travels through empty space, travels at the constant velocity of c. I call it my second postulate.

Us: But "velocity of c" with respect to what, Einstein?

Einstein: Well, since it is a law of optics, with respect to a reference system in which the laws of optics can claim validity.

Us: But what systems can the laws of optics claim validity in?

Einstein: Believe it or not, they can claim validity in the same systems that the laws of mechanics can claim validity in. The identification of the systems within which laws of mechanics (and consequentially laws of electrodynamics and optics) can claim validity is the job of my first postulate.

Us: How do you know that the laws of optics are the valid in the same systems that the laws of mechanics are valid in, Einstein?

Einstein: Good question. I know it because of this magnet and conductor illustration. (He shows us a magnet and conductor illustration, and we don’t quite see how it justifies his last assertion, but we continue).

Us: OK Einstein. So what systems can the laws of mechanics claim validity in?

Einstein: Don’t you know? The laws of mechanics can only claim validity in those systems which are in rectilinear and uniform motion with respect to one another.

Us: Why is that Einstein?

Einstein: Well, first you must understand that the laws of classical mechanics are based on the principle that a body will travel in uniform motion so long as it is not acted upon by an external force. This is called Galileo’s principle. We can consider such a body to be one which is far removed from all matter. If it is far removed from all matter, then there cannot be any gravitational forces acting on it. According to Galileo’s principle, this body must travel in uniform motion. That is, this body cannot accelerate. Therefore, this principle cannot be valid for reference systems within which this body accelerates. Rather, it can only claim validity in those systems within which the body is moving uniformly. If all of these systems are moving uniformly with respect to the body, then it follows that they are in rectilinear and uniform motion with respect to one another. Since Galileo’s principle can only hold good in one of a set of reference systems moving in rectilinear and uniform motion with respect to one another, and since classical mechanics is based on Galileo’s principle, it follows that all of classical mechanics can only hold good in one of a set of reference systems moving in rectilinear and uniform motion with respect to one another.

Us: OK, I’ve got it. So the laws of mechanics can only hold good in reference systems which are in rectilinear and uniform motion with respect to one another. And because of that magnet and conductor thing you mentioned, so, too, do the laws of electrodynamics and optics. And one of the laws of optics is the new law of optics which you created. It is your second postulate which says that light travels through empty space with the constant velocity of c. So if the laws of optics hold good in all reference systems which are in rectilinear and uniform motion with respect to one another, and if one of the laws of optics is that light travels through empty space at the constant velocity of c, then it follows that light travels through empty space at the constant velocity of c with respect to all reference systems which are in rectilinear and uniform motion with respect to one another.

Einstein: You’ve got it. That’s the very assumption upon which I created my SRT. But we have, so far, only considered the laws of classical physics. What we find is that the laws of mechanics (and consequentially the laws of electrodynamics and optics, which includes my second postulate) do in fact remain valid in all reference systems- not just those ones which move in rectilinear and uniform motion with respect to one another.

Us: What made you change your mind, Einstein?

Einstein: Well, I didn’t really change my mind. I just opened it up a little bit. What I had previously described to you were the laws of classical mechanics, which were based on Galileo’s principle. But then I started thinking critically about why it is that gravitational and inertial mass always have the same value. What I realized was that we have no right to say that gravitational mass and inertial mass aren’t simply the same thing, as looked at from two different points of view. This equivalence of inertial mass with gravitational mass I call "The Principle of Equivalence". Once this "Principle of Equivalence" is taken into account, we cannot say that Galileo’s principle is invalid in a reference system with respect to which a body, far removed from all matter, is accelerating. The reason for this is because we really have no right to say whether the body is accelerating for an unexplainable reason, as classical mechanics would have us believe, or if it is accelerating because there is a force acting on it.

Us: I’m a little bit confused. Can you explain that to me one more time?

Einstein: Sure. Assume that far removed from all matter there is a room on a spaceship. We attach a reference system to this room. Inside this room there is a man and a ball. We assume that the man is seat belted to a chair in the room but that the ball is freely moving. Galileo’s principle demands, since the room is so far away from all matter, and there are therefore no forces acting on the ball, that the ball just float in the room. The ball would indeed float in the room as long as the spaceship had its thrusters off. In such a case, Galileo’s principle could claim validity for the observer in the room and for the reference system attached to the room. However, if the spaceship is to turn its thrusters on, and the spaceship were to accelerate, then the ball would accelerate in the room. In such a case, Galileo’s principle, and the whole rest of classical mechanics, cannot be valid for the observer in the room, or for a reference system attached to the room. Such was the case before we considered the "Principle of Equivalence" which pointed us toward the interpretation that the laws of mechanics can only claim validity in reference systems which are in rectilinear and uniform motion with respect to one another. However, now the situation is different. Let us again consider the case where the spaceship turns its thrusters on and the ball falls down to the floor. Who are we to say that the ball does not fall to the floor because it is responding to some gravitational field? For the man would have no way to tell the difference, if he cannot look outside the spaceship. And if we can explain the falling ball in terms of responding to some gravitational field, then we do not need to discard the laws of mechanics for the reference system attached to the spaceship in such a case. Thus we find that laws of mechanics do indeed remain valid in all reference systems.

Us: OK Einstein. I think I’ve got it. But I have just one more question. Why can’t the man look outside of the spaceship?

"Classical Mechanics is based on Galileo’s principle: A body is in rectilinear and uniform motion as long as other bodies do not act on it. This statement cannot be valid for arbitrary moving systems of coordinates. It can claim validity only for so-called ‘inertial systems.’ Inertial systems are in rectilinear and uniform motion with respect to each other. In classical physics laws claim validity only with respect to all inertial systems (special principle of relativity). (The Theory of Relativity, A. Einstein, 1949)"

"…classical mechanics starts out from the following law: Material particles sufficiently far removed from other material particles continue to move uniformly or continue in a straight line of rest…this fundamental law can only be valid for bodies of reference K which possess certain unique states of motion, and which are in uniform translational motion relative to each other. Relative to other reference-bodies K the law is not valid. Both in classical mechanics and in the special theory of relativity we therefore differentiate between reference-bodies K relative to which the recognised ‘laws of nature’ can be said to hold, and reference-bodies K relative to which these laws do not hold. (Relativity, A. Einstein, 1961)"

Einstein believes that it has to be proven as to whether or not a law of physics is valid for an observer or in a reference system. The mechanical part of SPR states that the laws of classical mechanics can only claim validity in those systems which do not rotate or accelerate in translation with respect to one another.

The common example used to illustrate SPR (mechanics) is taken from a passage written by Galileo. In one of his works, Galileo commented on something he noticed about the motion of bodies in the cabin of a boat. What he noticed was that the motion of these bodies (with respect to the boat) was the same, provided that the boat did not accelerate on the water.

An equivalent thought experiment is also commonly used which considers, instead of the boat, a train. Two observers aboard a train can play catch with a ball, and a woman can pour her coffee, provided that the train does not accelerate on land.

Let us consider that an ice block is placed on the frictionless floor of a train. This ice block will not accelerate with respect to the train unless the train accelerates on land. But if the train brakes (i.e. decelerates), then the ice block will accelerate forward with respect to the train.

Let us first look at what Newton would say about the above situation, and then look at what Einstein says about the above situation.

Regardless of whether or not the train puts on its brakes, the acceleration of the ice block with respect to the earth is zero. This is because the earth only pulls the ice block down- not forwards or backwards. Newton would say that his laws only attempt to describe the motion of the ice block with respect to the earth (i.e. not the motion of the ice block with respect to the train). The motion of the ice block with respect to the train (or observers on the train), Newton would say, is circumstantial. In other words, Newton would say that his laws do not even begin to attempt to describe the motion of the ice block (i.e. test mass) with respect to the train.

But Einstein views this situation differently. Einstein believes that the laws of mechanics attempt to describe the motion of the ice block with respect to the train. According to Einstein, Newton’s first law (or as he calls it, Galileo’s principle) demands that the ice block not accelerate. This is because the earth does not pull it forward or backward. However, Einstein thinks that this "acceleration" is supposed to be taken with respect to the train (i.e. not the earth). Therefore, Einstein continues, laws of classical mechanics cannot be valid for an observer on the train (or in a reference frame attached to the train) when the train brakes (i.e. decelerates on earth).

"If the motion of the carriage is now changed into a non-uniform motion, as for instance by a powerful application of the brakes, then the occupant of the carriage experiences a correspondingly powerful jerk forwards. The retarded motion is manifested in the mechanical behaviour of bodies relative to the person in the railway carriage. The mechanical behaviour is different from that of the case previously considered, and for this reason it would appear to be impossible that the same mechanical laws hold relatively to the non-uniformly moving carriage, as hold with reference to the carriage when at rest or in uniform motion. At all events it is clear that the Galileian law does not hold with respect to the non-uniformly moving carriage. (Relativity, A. Einstein, 1961)"

The term "inertial reference frame" means "the reference frames which SRT considers" or "the reference frames identified in SPR". But what reference frames does SRT (SPR) consider (identify)? Well, we know that SRT (SPR) considers (identifies) only the reference frames which do not rotate or accelerate in translation with respect to one another. We also know that SRT (SPR) considers (identifies) only those reference frames within which the laws of classical mechanics (and classical physics) remain valid. But can we come up with a more physical description of these frames? Taylor and Wheeler, in Spacetime Physics, try.

Taylor and Wheeler say that SRT considers "free float" frames. Free float frames are any frames which are freely floating. For example, a spaceship in outer space would be freely floating if it does not have its thrusters on. An elevator on earth is freely floating if the cable has just broken and it is falling toward the ground where it will then smash. A ball inside of the non-thrusting spaceship will not accelerate with respect to the spaceship. A ball inside of the soon-to-smash-in-the-ground elevator will not accelerate with respect to the elevator.

Einstein’s SRT most definitely considers freely floating frames (the spaceship type) in outer space, but SRT most definitely does not consider freely floating frames (the elevator type) near earth. Einstein only considers these elevator type of freely floating frames in order to illustrate the logic behind his "Principle of Equivalence" which is a part of GRT but is not a part of SRT. (The logic behind Einstein’s "Principle of Equivalence" can be interpreted in more than one way and that is why I have not really dealt with it in this paper).

The spaceship type freely floating frames accelerate with respect to the elevator type freely floating frames and it was for this reason that Einstein went on to claim that laws of mechanics hold good in those frames which accelerate with respect to one another. If what Taylor and Wheeler are saying is true-that is, if it is true that SRT considers all free float frames- then, since free float frames can and do accelerate with respect to one another, why doesn’t SRT consider frames which accelerate with respect to one another?

In fact, Taylor and Wheeler circumvent even having to identify an SPR and a GPR. Rather, they just call Einstein’s first postulate his Principle of Relativity. Instead of saying how this postulate differs in GRT from SRT, they only describe it as if it means the same thing in SRT as it does in GRT. They describe it in a positive form and then in a negative form. Their positive form says "all the laws of physics are the same in every free-float (inertial) reference frame". Their negative form says "no test of the laws of physics provides any way whatsoever to distinguish one free-float frame from another". All of this stuff that Taylor and Wheeler mention has to do with GRT and not SRT. It has to do with Einstein’s "Principle of Equivalence" which is not a part of SRT.

By neglecting to identify the difference between SPR and GPR, Taylor and Wheeler circumvent having to answer to the uncomfortable question, "Why did Einstein, in 1905, believe that the laws of classical physics were not valid for observers which accelerate with respect to one another, or in reference systems which do not rotate or accelerate in translation with respect to one another?"