# Why did Einstein define speed of light as a constant and time as a variable?

#### EnumaElish

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Why did Einstein choose to define speed of light as a constant and time as a "variable" (relative to motion), rather than the reverse?

I am aware of experimental results confirming constant speed of light and time dilation. But Einstein did not have those results at the time he proposed SR as a theory. (I doubt he even had Morrison-Morley results, but I may be wrong on this point.)

What was (or would be) so different and so vastly more difficult in theoretical physics if one were to keep time constant (relative to motion) and treat the speed of light as any other speed in physics?

I guess my question is: what is a good source to look at to understand the inherent theoretical constraints that "forced" Einstein to re-define the concepts of time and lightspeed in radical contrast to Newtonian physics (including printed and Internet sources)?

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#### ZapperZ

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EnumaElish said:
Why did Einstein choose to define speed of light as a constant and time as a "variable" (relative to motion), rather than the reverse?
He didn't CHOOSE to keep time "variable". It came out of the first postulate that c is a constant in all reference frame. So one came out of the other.

As to why c is a postulated constant is a long discussion. At some point, Einstein realized that everything we observe and measure had an implicit assumption that the speed of light is instantaneous. Thus, when you remove that assumption and put a value to it, you can make a first postulate that c is constant everywhere and THEN, figure out the consequences to mechanics. This is when you get the time dilation, length contraction, etc.. etc. Everything else came out of a logical derivation of the postulates.

Zz.

#### dextercioby

Homework Helper
EnumaElish said:
Why did Einstein choose to define speed of light as a constant and time as a "variable" (relative to motion), rather than the reverse?
Because experimental evidence favored the first option.

EnumaElish said:
I am aware of experimental results confirming constant speed of light and time dilation. But Einstein did not have those results at the time he proposed SR as a theory. (I doubt he even had Morrison-Morley results, but I may be wrong on this point.)
WRONG ! He was very much aware of the experiments and theories before 1905.

EnumaElish said:
What was (or would be) so different and so vastly more difficult in theoretical physics if one were to keep time constant (relative to motion) and treat the speed of light as any other speed in physics?
Then you'd be forced to adopt the Newtonian view of a spacetime.

EnumaElish said:
I guess my question is: what is a good source to look at to understand the inherent theoretical constraints that "forced" Einstein to re-define the concepts of time and lightspeed in radical contrast to Newtonian physics (including printed and Internet sources)?
Einstein's orginal June 30 th 1905 "Zur Elecktrodynamik bewegter Körper" has it all. It has to do with Maxwell's equations.

Daniel.

#### chronon

Einstein would have known about the Michelson-Morley results in 1905, but he downplayed them as inspiration for SR. He reasoned that Newtonian dynamics were the same in moving frame of reference, but that Maxwell's equations of electromagnetism were not. He then looked at what could be changed to make Maxwell's equations invariant - the answer was to allow time and space to be relative. Others, such as Lorentz, had obtained similar results which showed that moving clocks would run slowly due to electromagnetic effects. Einstein realised that there was no way to say which clock was in fact moving, and so defined time as 'what is measured by a clock', so time in different frames would be different.

#### EnumaElish

Homework Helper
Chronon, thanks for your response -- among others who also responded. This question is unrelated to my orig. post, but here goes: do you remember where (which fiction book) you came across the phrase "somewhen"? I remember seeing it as I was leafing through a book in the Sci-Fi section (in a bookstore) well more than a year ago, but cannot remember the title or the author.

Is it from Time Traveler's Wife, or some other book?

#### jtbell

Mentor
chronon said:
Einstein would have known about the Michelson-Morley results in 1905, but he downplayed them as inspiration for SR. He reasoned that Newtonian dynamics were the same in moving frame of reference, but that Maxwell's equations of electromagnetism were not.
...using the transformation equations of classical (Galilean) relativity, of course.

He then looked at what could be changed to make Maxwell's equations invariant - the answer was to allow time and space to be relative.
That is, instead of changing Maxwell's equations to make them consistent with Galilean relativity, he left them as they were and replaced the Galilean transformation equations with a different transformation that does leave Maxwell's equations invariant. Since the equations of Newtonian mechanics are not invariant under the new transformation, Einstein had to replace Newtonian mechanics as well.

Others, such as Lorentz, had obtained similar results which showed that moving clocks would run slowly due to electromagnetic effects.
In fact, Lorentz had come up with the correct set of transformation equations for Maxwell's equations, which Einstein then applied to all of mechanics. That's why we call them the "Lorentz transformation" instead of the "Einstein transformation."

#### JesseM

jtbell said:
In fact, Lorentz had come up with the correct set of transformation equations for Maxwell's equations, which Einstein then applied to all of mechanics. That's why we call them the "Lorentz transformation" instead of the "Einstein transformation."
I've always wondered, what was Lorentz' physical interpretation of the relativity of simultaneity in the Lorentz transformation? Time dilation and Lorentz contraction could be explained as weird physical effects of an object's velocity relative to the ether, but that doesn't really work for the relativity of simultaneity...

#### EnumaElish

Homework Helper
The fantastic four (Lorentz, Maxwell, Einstein and Newton)

jtbell said:
In fact, Lorentz had come up with the correct set of transformation equations for Maxwell's equations, which Einstein then applied to all of mechanics. That's why we call them the "Lorentz transformation" instead of the "Einstein transformation."
Do you mean: "L. had come up with the transformation to render M's equations invariant. E. realized that ...
jtbell said:
... the equations of Newtonian mechanics are not invariant under the new transformation ...
... so E. said "I better apply the same transformation to Newtonian mechanics in general to make physics internally consistent again"?

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JesseM said:
I've always wondered, what was Lorentz' physical interpretation of the relativity of simultaneity in the Lorentz transformation? Time dilation and Lorentz contraction could be explained as weird physical effects of an object's velocity relative to the ether, but that doesn't really work for the relativity of simultaneity...
Did Lorentz even recognize the relativity of simulaneity in his transformations? AFAIK, he spoke of them as a mathematical trick, not physically meaningful.

#### JesseM

Did Lorentz even recognize the relativity of simulaneity in his transformations? AFAIK, he spoke of them as a mathematical trick, not physically meaningful.
Well, if he came up with the full equations of the Lorentz transformation, I think it's likely he would have noticed two events which have the same time-coordinate in one frame can have different time-coordinates in another. But you may be right that he just saw them as a mathematical trick. Didn't he think time dilation and Lorentz contraction had a physical meaning on their own, though?

#### jtbell

Mentor
EnumaElish said:
Do you mean: "L. had come up with the transformation to render M's equations invariant. E. realized that ...
Right!

... so E. said "I better apply the same transformation to Newtonian mechanics in general to make physics internally consistent again"?
No, E. said "I better invent a new mechanics that is invariant under the Lorentz transformation."

#### chronon

EnumaElish said:
Chronon, thanks for your response -- among others who also responded. This question is unrelated to my orig. post, but here goes: do you remember where (which fiction book) you came across the phrase "somewhen"? I remember seeing it as I was leafing through a book in the Sci-Fi section (in a bookstore) well more than a year ago, but cannot remember the title or the author.

Is it from Time Traveler's Wife, or some other book?
I don't think that I came across it in a book. I do remember a relativity lecture in which the lecturer called the spacetime outside the forward and backward light cones of an event "elsewhen".

#### laylo

I haven't read all these replies, but I am wondering, what exactly did Einstein mean by that comment?

#### Ich

I think the most important point is that Einstein extended the relativity principle to electrodynamics. Of course it has always been there, hidden by the artificial splitting into electric and magnetic fields.
Every attempt to keep a global time destroys this symmetry - while it is still there in all observations. That's where Occam's razor tells us to prefer SRT over Lorentz's interpretation.

#### HallsofIvy

Homework Helper
The Michelson-Morely experiment was first done in 1887, 28 years before Einstein's paper- of course he knew about that- probably studied it as an undergraduate. I have no idea what "Morrison-Morely" is and can't find any reference to it on google.

#### Jimmy Snyder

A brief history of relativity.

Newton: You can't tell how fast you are going.
Maxwell: Yes, you can.
Einstein: No, you can't.

#### rbj

Why did Einstein choose to define speed of light as a constant and time as a "variable" (relative to motion), rather than the reverse?
although a postulate, it wasn't an arbitrary "definition". Einstein didn't just pull this idea out of his butt.

I am aware of experimental results confirming constant speed of light and time dilation. But Einstein did not have those results at the time he proposed SR as a theory. (I doubt he even had Morrison-Morley results, but I may be wrong on this point.)
i think you are. but also i think that Einstein was not surprized at the result. he had these neat "thought experiments" ("as if God had any choice in the matter") and he would have been greatly disconcerted if it came out differently than it had.

What was (or would be) so different and so vastly more difficult in theoretical physics if one were to keep time constant (relative to motion) and treat the speed of light as any other speed in physics?

I guess my question is: what is a good source to look at to understand the inherent theoretical constraints that "forced" Einstein to re-define the concepts of time and lightspeed in radical contrast to Newtonian physics (including printed and Internet sources)?
don't have a book, but i try to paraphrase Einstein's thought experiment below. jimmysnyder sums it up nicely:

A brief history of relativity.

Newton: You can't tell how fast you are going.
Maxwell: Yes, you can.
Einstein: No, you can't.
... in a vacuum. but you can tell how fast you are accelerating.

for me, the postulates that no inertial frame is qualitative different (or "better") than any other inertial frame of reference and that we can't tell the difference between a "stationary" vacuum and a vacuum "moving" past our faces at a high velocity, that there is no difference and that Maxwell's Equations should work the same for any and all inertial frames so then the speed of E&M must be measured to be the same in all inertial frames, even if it is the same beam of light viewed by two observers moving relative to each other. from that, we got time dilation, then length contraction, then Lorentz transformation, and so on.

besides the fact that there was a very important experiment, the Michealson-Morley experiment, where they were specifically looking for evidence of a change in the speed of light, given the realistic assumption that if the aether existed, our planet oughta be moving through it at least some season of the year and at sufficient speed that they could measure the difference in c parallel to this movement and perpendicular to this movement and the experiment came out negative . no such change in c was detected. besides that experimental fact, Einstein had a thought experiment about it that i paraphrase below:

you understand that "light" is the propagation of electromagnetic (E&M) fields or "waves" and the physics that describes that propagation are "Maxwell's Equations").

i would not call the constancy of c (for all frames of reference) an axiom or postulate for which there is no idea why such principle exists (and we just notice it experimentally). it's because we can detect no intrinsic difference between different inertial frames of reference (as jimmysnyder alludes to, two observers moving at constant velocities relative to each other both have equal claim to being "stationary", there is no good reason to say that one is absolutely stationary and the other is the one that is moving) and that the laws of physics, namely Maxwell's equations, apply to both frames of reference equally validly. if two different observers, neither accelerated but both moving relatively to each other, are examing the very same beam of light (an electromagnetic wave), for both observers, when they apply and solve Maxwell's equations for the propagation of the EM wave, they both get the same speed of c out of solving Maxwell's eqs.

so we do have a good idea for why the speed of propagation of E&M is the same for all inertial observers that may or may not be moving relative to each other. it's because, we cannot tell the difference between a "moving" vacuum and "stationary" vacuum, that there is no difference between a moving and stationary vacuum and then there is not apparent reason for the observed speed of light to be different.

this is different than for sound. the physics of Maxwell's Equations make no reference to a medium that conducts the electromagnetic field (and, indeed, the Michaelson-Morley experiement failed to show that such a hypothetical medium, called "aether" exists - if it does exist, it seems to be moving around in the same frame of reference as the Earth going around the sun because no matter what time of day or season of the year, no one could detect with the M-M apparatus any motion through this aether). but for sound, the physics describe it as compressions and rarefractions of the air (or whatever other matter medium). there is no such thing as sound in a vacuum (but there is light). so if you feel the wind moving past your face from left to right (say at a speed of 20 m/s), you will also measure the speed of sound from a source on your left to be 20 m/s faster than sound from a source in front of you and 40 m/s faster than a sound that is at your right. now you can repeat that setup and get an identical result if there is no wind but you are moving (toward your left) through the air at a speed of 20 m/s. so the observer that is stationary (relative to the air) will look at a sound wave and measure it at something like 334 m/s, but you, moving through the air toward the source at 20 m/s will measure the speed of that very same sound wave to be 354 m/s.

now think of the same thing, but instead you two observers are out in some vacuum of space somewhere and are looking at the same beam of light. the other observer is holding the flashlight and measuring the speed of light to be 299792458 m/s. you are moving toward that observer at a speed of, say, 1000 m/s and looking at the very same beam of light that the other observer is. you are thinking that you would measure it at a speed of 299793458 m/s, right? but why should it be any different for you? you have equal claim to being stationary (and it's the guy with the flashlight is moving toward you at 1000 m/s). you cannot feel the vacuum moving past you at a speed of 1000 m/s, in fact there is no physical meaning to the vacuum moving past your face at 1000 m/s like it's a wind. you cannot tell the difference between you moving and the other guy as stationary or if the roles were reversed and there is no meaning to any notion of who is stationary absolutely and who is moving.

so then, if there is no meaningful difference, if both of you have equal claim to being stationary (and it's the other guy that is moving), then the laws of physics (particularly Maxwell's Equations) have to be exactly the same for both of you, both in a qualitative sense, and in a quantitative sense. both of you have the same permittivity of free space ($\epsilon_0$) and permealbility of free space ($\mu_0$). so when you apply Maxwell's equations to this E&M wave (of this flashlight beam), you will see that this changing E field is causing a changing B field which, in turn, is causing a changing E field which is causing a changing B field, etc. now for both of you, the laws (Maxwell's Eqs. and the parameters $\epsilon_0$ and $\mu_0$) are the same. then it turns out, when we solve Maxwell's Equations for this case, we get a propagating wave and the wave speed is

[tex] c = \sqrt{\frac{1}{\epsilon_0 \mu_0}} [/itex]

but that's the same for both you and the other observer!! (even though you are both moving relative to the other.) there is no reason that the other guy should solve the Maxwell's equations and get a different $c$ than you get (because you have the same $\epsilon_0$ and $\mu_0$)! even if you two are looking at the very same beam of light.

the expired equine lies beaten and bleeding.

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#### Jimmy Snyder

... in a vacuum. but you can tell how fast you are accelerating.
I'm not sure, but I don't think you can tell how fast you are going even when you are not in a vacuum. Also, I thought that the equivalence principle implies that you can't tell if you are accelerating either.

#### rbj

right on both counts

I'm not sure, but I don't think you can tell how fast you are going even when you are not in a vacuum.
but, in a non-vacuum, you can tell how fast you are going relative to the stuff of your environment.

Also, I thought that the equivalence principle implies that you can't tell if you are accelerating either.
okay, you're correct in the Euclidian sense. i'm either sitting in my chair on Earth and not accelerating, or this push i feel on my butt is because i'm accelerating upward at 9.8 m/s2.