Some questions about light and relativity

[thetexan]

I'm trying to study on light velocity and relativity. And I have a few questions I hope someone can make clear to me. Please try to not use math but just explain in layman's terms if possible.

I know the light is measured at the same speed regardless of the observer. Why? More to my point...why is light special in this regard? Is it due to the velocity?

For example...if apples traveled at the speed of apples, 182,000 mps would they be measured at the same velocity regardless of the observer? Is it the velocity that makes it so?

Or...is it something about the THING that is doing the traveling at 182,000...that is, light...that makes this so? In which case, if light maxed out at 100,000 mps would we see the same effect?

Is it that light is the fastest carrier of information that makes it so? I know this is hypothethical but what if we could transmit thoughts and thoughts were found to travel at 500,000 mps would that make them obedient to the same idea that the thought speed will always be measured at 500,000 mps regardless of the frame of observance?

In other words, does "same measured velocity, regardless of the observer" principle apply only to light or would it apply to anything that would go that fast, with light just happening to be the fast thing in our universe?

What about light makes this principle particular to light? Would an apple traveling at .99 the speed of light seem to be .99c to any observer or would velocity be cumulative? If I was in a car traveling at .5c and threw a baseball backward at .99c would an observer measure the ball at .49c?

Again, what characteristic about this thing we call light that makes it obedient to this principle when nothing else is?

This may be confusing but I wonder about this.

thanks
tex

 

[.Scott]

I know the light is measured at the same speed regardless of the observer. Why? More to my point...why is light special in this regard? Is it due to the velocity?

Yes, it is due to the velocity. It is part of the basic geometry we live in.

For example...if apples traveled at the speed of apples, 182,000 mps would they be measured at the same velocity regardless of the observer? Is it the velocity that makes it so?

The speed of light is about 186,000 miles per second. The answers to your questions is "yes". However, the observed mass of apples traveling at the speed of light would destroy the observer. Perhpas we should stick to 182,000 mps after all. In this case, the difference between light and apples is simply that apples have a real rest mass. Photons (light particles) have zero rest mass.

Or...is it something about the THING that is doing the traveling at 182,000...that is, light...that makes this so? In which case, if light maxed out at 100,000 mps would we see the same effect?

As I said before, it is the basic geometry of the universe we live in. If that geometry was change to make the limit 100,000 mps, then I would guess that particles with a rest mass of zero would travel at that limit.

Is it that light is the fastest carrier of information that makes it so? I know this is hypothetical but what if we could transmit thoughts and thoughts were found to travel at 500,000 mps would that make them obedient to the same idea that the thought speed will always be measured at 500,000 mps regardless of the frame of observance?

The current thought is that information cannot be transmitted at faster than the speed of light - that is, faster than the basic geometric limit. Since "thoughts" are part of our geometry and contain information, that limit would apply to thoughts. I would quickly add, that this message board is an example of transmitting thoughts. Let's stick to the less speculative thought-transmission methods.

In other words, does "same measured velocity, regardless of the observer" principle apply only to light or would it apply to anything that would go that fast, with light just happening to be the fast thing in our universe?

Applies to anything.

What about light makes this principle particular to light? Would an apple traveling at .99 the speed of light seem to be .99c to any observer or would velocity be cumulative? If I was in a car traveling at .5c and threw a baseball backward at .99c would an observer measure the ball at .49c?
Again, what characteristic about this thing we call light that makes it obedient to this principle when nothing else is?

I think I answered this before. But the basic difference is that photons have no rest mass. You wanted to avoid formulas here, but there are formulas for adding and subtracting relativistic speeds - those that are significant fractions of the speed of light. Those equations apply to everything.

 

[Nugatory]

In other words, does "same measured velocity, regardless of the observer" principle apply only to light or would it apply to anything that would go that fast, with light just happening to be the fast thing in our universe?

Anything that moves at speed $c$. Light was the first thing that was observed to move at this speed, which is why we call it "the speed of light", although it would be more accurate to call it "the universal invariant speed".

Would an apple traveling at .99 the speed of light seem to be .99c to any observer or would velocity be cumulative? If I was in a car traveling at .5c and threw a baseball backward at .99c would an observer measure the ball at .49c?

. No, because speeds don't add and subtract that way. If you are in a car moving at speed $u$ relative to the ground and you throw a ball ahead at speed $v$ relative to the car, the speed of the ball relative to the ground will not be $u+v$, it will be $\frac{u+v}{1+uv/c^2}$.

 

[thetexan]

The masslessness of photons are the key obviously, at least to photons BEING ABLE to travel at that speed. It's the "same speed measured in any frame of reference" issue that escapes me. I guess I still wonder about why light? Let me ask it another way...

If, in a different life, there were some other THING besides light that traveled at the speed of that thing and that speed was the ultimate speed, would relativity dictate that that thing moving at its maximum speed would always be measured the same regardless of frame of reference? When other things the speed adds or subtracts such as the baseball. If something comes out of the headlight fixture of a rapidly moving automobile then that thing's velocity is added to that of the automobile. But if that thing is light then is does not...rather it comes out at its max speed as observed by the driver...AND as observed by the guy on the street. This makes the phenomena of light unusual in a way that is different from the other thing coming out of the headlight fixture. And it just seems to me that that difference has to do with something other than the masslessness of light, which simply allows it to travel fast. It doesn't seem to me (which is not saying much) that the masslessness has anything to do with the "same speed as measured from any frame of reference" issue. Maybe it has to do with the wave nature of light.

tex

 

[SiennaTheGr8]

Anything that can travel at the speed of light can only travel at the speed of light. No faster, no slower. The only things that behave this way are massless.

Everything else has mass and must always travel slower than the speed of light.

 

[thetexan]

Anything that can travel at the speed of light can only travel at the speed of light. No faster, no slower. The only things that behave this way are massless.

Everything else has mass and must always travel slower than the speed of light.

Absolutely. I understand that part.

My question is what is the reason that light (which can travel at 100%c because of all of the above) is always observed to be at the speed of light regardless of reference frame.

A rocket is going forward at 100000mph. An astronaut shines a flashlight to the rear. As far as the astronaut is concerned the speed of the beam is 186000mps. A bystander sees the beam as 186000mps when with other objects the speed would seem slower. I understand that. My question is why should that be with light. What makes light special that it lives by its own velocity rule apart from all other objects? What is the attribute of the phenomena of light that makes this so? I understand that it will never go FASTER.

Why doesn't sound have whatever this attribute is. That's not just a kindergarten question. Sound's velocity is additive or subtractive, light is not. What is the difference between these two that accounts for that. Sound propagates thru a medium, light does not. But they both propagate...each leave here and propagate to there. Why shouldn't the "same speed regardless of reference frame" principle apply to either? Is it because of the vast difference in velocity? Is it that as something goes faster and approaches relativistic speeds the "same observed velocity" principle becomes more pronounced until ultimately we reach the ultimate relativistic speed (which happens to also be the speed of light, 186,000mps) at which point the "same observed velocity" principle is at its 100% point? If this is true then is it that it's not light itself that is the reason for the principle of
"same velocity regardless of observed reference frame"...it's the fact that the THING has reached the ultimate relativistic velocity...and light just happens to be the only thing that can go that fast?

It seems to me that it's the velocity that is the key to the "same measured speed regardless of frame of reference" principle and that light just happens to be the THING that travels that fast...that CAN travel that fast because of its masslessness.

Is this on the right track? I know this is hard to explain to a layman like me and I appreciate your patience.

tex

 

[Janus]

The masslessness of photons are the key obviously, at least to photons BEING ABLE to travel at that speed. It's the "same speed measured in any frame of reference" issue that escapes me. I guess I still wonder about why light? Let me ask it another way...

If, in a different life, there were some other THING besides light that traveled at the speed of that thing and that speed was the ultimate speed, would relativity dictate that that thing moving at its maximum speed would always be measured the same regardless of frame of reference? When other things the speed adds or subtracts such as the baseball. If something comes out of the headlight fixture of a rapidly moving automobile then that thing's velocity is added to that of the automobile. But if that thing is light then is does not...rather it comes out at its max speed as observed by the driver...AND as observed by the guy on the street. This makes the phenomena of light unusual in a way that is different from the other thing coming out of the headlight fixture. And it just seems to me that that difference has to do with something other than the masslessness of light, which simply allows it to travel fast. It doesn't seem to me (which is not saying much) that the masslessness has anything to do with the "same speed as measured from any frame of reference" issue. Maybe it has to do with the wave nature of light.

tex

Both the baseball and and light behave by the same rule for the addition of velocity, the one already given by Nugatory.
If you throw a ball forward (relative to you) at 0.25c while traveling at .5c relative to someone else, you measure the balls speed as 0.25 and he will measure it as being 0.666.. c (not 0.75 c as you would expect using Newtonian velocity addition.)
If you throw the ball at .35c, the you get 0.35c and .7234c.
If we graph the results as you throw the ball faster, you get the following:

The blue line is the velocity you measure for the ball and the red line the other observer's measurement of its velocity (you are moving at 0.5 relative to the observer. Note how your velocity measurement and that of the observer converge as you throw the ball at a speed closer and closer to c, until, at c they become the same. (you wouldn't really wouldn't be able to throw a massive object exactly at c, but you could get so close to it that the difference between the two velocity measurements is as close to zero as you want.)
So yes, it is the speed, (and the fact that light, being mass-less travels at it) that determines why light has the same velocity as measured by everyone.

 

[.Scott]

If, in a different life, there were some other THING besides light that traveled at the speed of that thing and that speed was the ultimate speed, would relativity dictate that that thing moving at its maximum speed would always be measured the same regardless of frame of reference?

This "different life", presumably lived in a "different universe" is a pretty sketchy construct.
In this universe, we have neutrinos. Neutrinos are nearly mass-less, but as best physics can tell, neutrinos have mass. They travel very close to the speed of light. So close, that the difference has yet to be measured. They appear to travel at the speed of light in all actual observations.

When other things the speed adds or subtracts such as the baseball. If something comes out of the headlight fixture of a rapidly moving automobile then that thing's velocity is added to that of the automobile. But if that thing is light then is does not...rather it comes out at its max speed as observed by the driver...AND as observed by the guy on the street. This makes the phenomena of light unusual in a way that is different from the other thing coming out of the headlight fixture. And it just seems to me that that difference has to do with something other than the masslessness of light, which simply allows it to travel fast. It doesn't seem to me (which is not saying much) that the masslessness has anything to do with the "same speed as measured from any frame of reference" issue. Maybe it has to do with the wave nature of light.

tex

Since cars and headlights can't travel very fast, let's use better examples. Say we put some radioactive ions into a particle accelerator and get ithem going at 99% the speed of light (0.99c). Then one of them decays and emits a neutrino. From the point of view of the other ions, that neutrino may be moving forward at over 0.9999c. So you might expect that the scientists would see that neutrino moving forward at 0.99c + 0.9999c. But they do not. They see it moving at close to the speed of light (over 0.9999c, but less than 1c).

 

[thetexan]

Both the baseball and and light behave by the same rule for the addition of velocity, the one already given by Nugatory.
If you throw a ball forward (relative to you) at 0.25c while traveling at .5c relative to someone else, you measure the balls speed as 0.25 and he will measure it as being 0.666.. c (not 0.75 c as you would expect using Newtonian velocity addition.)
If you throw the ball at .35c, the you get 0.35c and .7234c.
If we graph the results as you throw the ball faster, you get the following:
View attachment 205813
The blue line is the velocity you measure for the ball and the red line the other observer's measurement of its velocity (you are moving at 0.5 relative to the observer. Note how your velocity measurement and that of the observer converge as you throw the ball at a speed closer and closer to c, until, at c they become the same. (you wouldn't really wouldn't be able to throw a massive object exactly at c, but you could get so close to it that the difference between the two velocity measurements is as close to zero as you want.)
So yes, it is the speed, (and the fact that light, being mass-less travels at it) that determines why light has the same velocity as measured by everyone.

AH HAAAAA! EUREKA! It IS the velocity that is the key! Thanks for the chart. That helped. As velocity increases toward the ultimate relativistic velocity the "observed velocity being the same in all frames of reference" principle becomes more pronounced until when we reach the ultimate velocity all observers in all frames of reference measure the same velocity. Conversely, as the speed reduces the greater the difference in observed speeds in different frames of reference...so much so that at tiny speeds (relative to light) the velocity is altogether additive or subtractive, or at least the math is simple addition or subtraction.

So if ANYTHING reaches the speed of light, even apples (if they could)...as they get faster and faster...and because of the velocity factor...different observer's measurements become closer to "the same velocity regardless of frame of reference" until eventually even apples will have the same max speed regardless of frame of reference. The issue then becomes simply...what can or cannot actually attain that speed due to its mass...apples can not. Photons can.

I think I've got it. The chart was the key. Thanks
tex

 

[Nugatory]

If, in a different life, there were some other THING besides light that traveled at the speed of that thing and that speed was the ultimate speed, would relativity dictate that that thing moving at its maximum speed would always be measured the same regardless of frame of reference?

No need for a different life - gravitational waves (the stuff that LIGO recently measured) move at the speed of light and have the same property of moving at that speed in all inertial reference frames.

 

[SiennaTheGr8]

What you're calling the "observed velocity being the same in all frames of reference" principle applies only to massless things. The wording you're using suggests that it's a property of an object that gets increasingly pronounced as that object gains speed, but I don't think that's accurate or helpful.

The whole point of relativity is that all inertial frames of reference are valid, so if something is traveling at .9999999c in one frame of reference, then there's another frame of reference in which it's at rest, and there's another frame of reference in which it's traveling at .2c in the opposite direction, and so on. Not so with light!

In other words, "observed velocity being the same in all frames of reference" isn't a matter of degree. Either something is massless and travels at c for all observers, or it has mass and takes on every possible sub-luminal velocity (just depends on the observer's frame of reference).

Yes, the relativistic velocity-composition law says that velocities aren't additive, and that they're only approximately so at low speeds. But I wouldn't view this as an explanation for why the speed of light is invariant. That strikes me as entirely backward, actually. The existence of a universal speed limit is the starting point. It's the only counterintuitive postulate you must accept in special relativity. Everything else (including the non-additivity of velocities) follows from that.

It's decidedly not the case that an object's velocity gets closer to becoming invariant as its speed increases.

 

[thetexan]

Oh, I accept the universality of the speed of light. No question there. And I understand that the only reason light (photons) can travel at that speed is because on their zero mass. That is why we associate light with that speed and speed limit. As it happens. As was stated gravitational waves also travel at that speed. I didn't as this question but I just thought of it...do gravitational waves appear to travel at 1c regardless of the observers frame of reference just like light? If a gravitational wave left the gravitational wave fixture on the front of a fast traveling rocket would the astronaut measure the speed at 1c? And would a stationary observer of the passing rocket observe the gravitational wave emitting from the front end of the rocket at 1c?

Does the property of light which says that the relative velocity of a beam of light is the same (1c) for any observer in any frame of reference apply to gravitational waves? This is the root of my question. With gravitational waves we have a non-photon, non light THING traveling at 1c. If the property of light that makes its velocity 1c regardless of frame of reference is velocity itself and not the photons then it would follow that gravitational waves would enjoy the same effect. I'm not sure if it does or not since I just thought of this.

The fact the photons, of all the objects in the universe ie apples, bullets, sound, planets, pizzas, are solely able to travel at this max speed because of their zero mass only goes to why light (photons) happen to be the objects associated with this speed. Photons go 1c. Is 1c the max because of the photon's native propensity to travel that fast...or...are photons restricted to that speed because that speed is, in and of itself, the max speed and all things are constrained to it?

In any case, I understood the above chart to mean that as speed approaches 1c the more the velocity of an object will appear to be the same regardless of frame of reference. And since light achieves 1c it appears the same in all frames of reference. If I understand it correctly, the baseball thrown forward from the front of a moving car will seem to be additive, that is, the 20 miles per hour of the ball will add to the 40mph of the car so that the drivers sees a ball velocity of 20mph and the guy on the side of the street will observe 60mph. Now as the speed of the ball is faster this will change. If the ball is thrown forward at 100000mps then the driver observes a ball velocity of 100000 mps and the guy on the side of the street sees 100000.0000004 mps. 100000.0111 would be 100000mps plus 40mph but because the ball is traveling at a high relativistic speed the additive part, the .01111, is reduced approaching zero. So that when the ball eventually is thrown forward at 186000mps then both the driver and the guy on the street observe 186000. This is what I mean by velocity being the determining factor for the phenomena of the massless photon objects being measured at 1c regardless of frame of reference. The closer to 1c the more the effect of relative speed measurements...and the slower the speed the less of the effect until at automobile speeds the objects velocity is additive.

That's what I understood from the chart and explanation. If that is wrong then I still would like to know what makes light special. If there were a massless particle that travels at .5c would the driver of the car and the guy on the street each measure the particle's velocity at .5c or would the guy on the street see some added velocity from the forward moving car?

Here is a thought experiment or question...Einstein did it so I'll use the method.
To illustrate this let's assume several massless particles shot forward from a fast moving rocket with an observer on a nearby asteroid

Dave Particle-----its natural velocity is .5c------ astronaut sees .5c----- observer sees .5c + some of the added velocity of the rocket
Sue Particle-------its natural velocity is .7c------astronaut sees .7c------observer sees .7c + less of the rocket velocity added
Dave Up Particle-----its natural velocity is .9c-------astronaut sees .9c -----observer sees .9c + almost none of the rocket's velocity added
Photon------its natural velocity is 1c.---------astronaut sees 1c------ observer sees the same universal velocity

As the velocity increases the added velocity factor reduces from completely additive (at automobile speeds) to completely universal with no additive factor.

That's what I mean by a gradual move from what we observe at slow speeds to what we observe at 1c.

So, now that I have tried to explain my understanding here is my question...

Is the velocity of light itself the reason why we observe a universal speed? If not, again, what is it about a beam of light that makes it different from other objects other than velocity. Mass just explains WHY photons can attain that speed. If I understand correctly, if I could make a baseball massless then it also could attain the max speed.

tex

 

[Janus]

As the velocity increases the added velocity factor reduces from completely additive (at automobile speeds) to completely universal with no additive factor.

Even at automobile speeds the velocities are not directly additive, it is just that the difference between adding them directly and adding them correctly is very small.
So for example, if you had an automobile driving at 100 kph, and threw a ball forward at 100kph, someone standing along the roadside would measure the ball moving at ~199.999999999998 kph, and not 200 kph. The only time they would add directly is when one of the velocities being added is zero.

In practice we can get away with using direct addition at normal everyday speeds just because the difference is so minute.

 

[Mister T]

If, in a different life, there were some other THING besides light that traveled at the speed of that thing and that speed was the ultimate speed, would relativity dictate that that thing moving at its maximum speed would always be measured the same regardless of frame of reference?

Anything that moves at speed $c$ does so in all frames of reference. As recently as the 1990's it was thought that neutrinos traveled at this speed, but it now seems clear that they don't. And even if it were discovered that light doesn't travel at speed $c$ we'd just call $c$ something other than the speed of light.

The first thing to wrap your head around is that if there's a speed that's the same in all reference frames then that speed has to be the fastest possible speed. Imagine chasing something moving at speed $c$ such as a beam of light, for example. No matter how fast your chase it'll still recede from you at speed $c$. Thus it's not possible for you to reach a speed of $c$.

 

[thetexan]

I think I understand. I may be saying differently but speed is the factor.

thank you
tex

 

[SiennaTheGr8]

You're basically right in a lot of ways, but you keep slipping in wording that suggests you may be misunderstanding some things.

It's not that photons can "achieve" the maximum speed: they are constrained to travel at that speed. What so constrains them is their masslessness. Any free massless particle will likewise be constrained to travel at c, although no kind other than the photon has been proven to exist.* The same is true of any massless system more generally, and so we can apply this reasoning to electromagnetic and gravitational radiation: EM and gravitational waves are massless and travel at c. Well, that goes for idealized unidirectional waves, at least—it gets more complicated when you take, say, a whole spherical wave as your system, which is why it's easier to talk about photons than EM waves in this context.

*(It used to be thought that neutrinos are massless, but now we know they aren't. If gravitons exist, they travel at c. Gluons are massless but are never "free," as I understand it.)

Similarly, nothing with mass can ever travel at the speed of light. Your guy driving the car can never throw the ball at c from anyone's perspective.

If I observe Dave traveling at .99999c and he shoots a bullet in the same direction at .00001c relative to himself, then yes, I'll observe the bullet traveling at a speed less than 1c (the velocities don't add). But it's just as valid to observe Dave in a frame of reference in which he himself is only traveling .00001c ("only"—hehe). In this frame, the bullet's speed is very very close to .00002c (the velocities approximately add). The "degree" of non-additivity is determined entirely by the frame of reference of the observer, which is arbitrary.

 

[Umaxo]

I don't think "it moves with c (speed of light) because it is massless" is good explanation. As far as i know, massless (i.e. rest mass is equal to zero) is defined as mass of the object that moves with c. You cannot actually measure rest mass of photon so the logic is not massless=>speed of light but rather opposite speed of light => massless. Massless is only definition/mathematical extrapolation and not physical reality.

As was explained, and as OP understood, the kye is the velocity and not light per se (am i using the word right?).
I don't think any attempt to show why it is light in particular that moves with such speed can have any reasonable explanation. It is like asking why electron in praticular is charged. That is the way it simply is and we must accept it.

Of course, we can then ask what concepts it connects together , i.e. going into field theories and showing how this fact is manifested in the mathematical structure and with what mathematical facts it is equivalent. Like f.e. - because electromagnetic force interacts with 1/r^2 far away from the source, the wave solution must lead to waves with speed of light etc. and that could be satisfactory explanation for some...But when one starts to think about it, the mathematical structure is simply made to fit that fact, because we have observed the fact.

I like to stand corrected if i am wrong though.

 

[SiennaTheGr8]

Consider these two equations:

$E = \dfrac{mc^2}{\sqrt{1 - \beta^2}}$

and

$\vec p = \dfrac{m \vec v}{\sqrt{1 - \beta^2}}$

According to these equations, anything without mass has zero energy and momentum, and anything that travels at the speed of light ($\beta = 1$) has undefined energy and momentum (division by zero). The only way out is if both conditions are simultaneously satisfied: $m = 0$ and $\beta = 1$. Then we get the indeterminate form $E = | \vec p | = 0/0$, which tells us nothing useful but also doesn't preclude a non-zero finite value for $E$ and $| \vec p |$.

Anything massless travels at the speed of light, and anything traveling at the speed of light is massless.

[edited]

 

[Dale]

As far as i know, massless (i.e. rest mass is equal to zero) is defined as mass of the object that moves with c.

Mass is defined as $m^2=E^2-p^2$ (in natural units). So massless is $E^2=p^2$

 

[Ibix]

...so yes, saying something has zero mass is the same as saying it moves at lightspeed, and vice versa.

 

[phinds]

I think I understand. I may be saying differently but speed is the factor.

Not sure what you mean but I'd say no, speed is NOT the factor. Mass is the factor. As has already been pointed out, the universal speed limit only applies to things that are massless and either something is massless or it is not.

 

[jbriggs444]

...so yes, saying something has zero mass is the same as saying it moves at lightspeed, and vice versa.

To split hairs, although it is true that anything that is massless moves at the speed of light and vice versa, saying that "massless" is defined as "moves at the speed of light" would not be correct.

The definition of massless is "has zero mass"
The definition of mass is the norm of the energy-momentum four-vector or, as @Dale has indicated: $m^2 = E^2-p^2$.

Must be my mathematics background peeking out. The phrase "by definition" always makes me suspicious.

 

[Umaxo]

Mass is defined as $m^2=E^2-p^2$ (in natural units). So massless is $E^2=p^2$

That is actually very helpfull. I never even realized that what i was interpreting as rest mass was complete nonsense. Thanks:)

 

[pixel]

The first thing to wrap your head around is that if there's a speed that's the same in all reference frames then that speed has to be the fastest possible speed. Imagine chasing something moving at speed $c$ such as a beam of light, for example. No matter how fast your chase it'll still recede from you at speed $c$. Thus it's not possible for you to reach a speed of $c$.

Is there an argument for the converse - if there's a fastest possible speed then it has to be the same in all reference frames?

 

[Nugatory]

Is there an argument for the converse - if there's a fastest possible speed then it has to be the same in all reference frames?

Yes. There are only two possibilities: there is no fastest possible speed, and inertial frames are related by the Galilean transformation; or there is one fastest possible speed, and inertial frames are related by the Lorentz transformations. Other possibilities can be excluded because they lead to internal contradictions.

 

[Mister T]

Is there an argument for the converse - if there's a fastest possible speed then it has to be the same in all reference frames?

If there's a speed that's different in different reference frames then it can't be the fastest possible speed. You would always be able to find a reference frame where that speed is larger.

 

[tophatphysicist]

Sketch A. The black coordinates observer is at rest in his black coordinate system and remains in position X1 = 0 as he moves straight forward into time along his X4 coordinate. The observer in the red coordinate system remains at rest in red position X1 while moving straight into time along his red X4 coordinate. We show here the red observer in motion at a significant percentage of light speed (perhaps around 0.5C) with respect to the “rest” black coordinates. The black observer sees the red observer moving along a continuous succession of points along the red X4 coordinate. Notice that, using Lorentz transformations, the red observers spatial X1 coordinate is rotated at an angle to the black X1 coordinate that is symmetric with respect to the rotation of the red X4 coordinate to the black X4 coordinate. This gives the red observer a different instantaneous 3-D cross-section view of the 4-D universe than that of the black observer. That is, the red observer sees a cross-section of the universe along his red X1 axis, whereas the rest black system observer sees instantaneous cross-sections of the universe along his black X1 axis.

Sketch B. Now we see the progression in the rotation of the X1 and X4 coordinates with respect to the black coordinates as observers move faster and faster. The blue observer moving along his own blue X4 coordinate is moving faster than the red observer, and blue’s X1 coordinate accordingly rotates to maintain the rotational symmetry.

So, what happens in the limit as an observer’s speed with respect to the black rest coordinates approaches the speed of light? In the limit the X4 coordinate and the X1 coordinate rotate toward each other, both reaching the 45 degree angle in the limit: The angle of a 4-dimensional photon. Thus, we have a geometrically unique orientation for any object moving at the speed of light. The green world line then represents a photon moving at the speed of light in all three coordinate systems. Note that as a result of the symmetric angles for the X1's and X4's in all coordinate systems, the ratio of the X1 to X4 for the photon line assures that all observers will find a ratio of 1:1 between X1 and X4.

 

[Mister T]

That is actually very helpfull. I never even realized that what i was interpreting as rest mass was complete nonsense. Thanks:)

It is best to adopt the modern terminology and refer to it simply as the mass. There is no other kind of mass used in the modern lexicon so there is no need to preface it with "rest" to distinguish it. The history of relativistic physics gave rise to terms that we no longer use: relativistic mass, transverse mass (which is identical to relativistic mass), and longitudinal mass.

 

[Umaxo]

It is best to adopt the modern terminology and refer to it simply as the mass. There is no other kind of mass used in the modern lexicon so there is no need to preface it with "rest" to distinguish it. The history of relativistic physics gave rise to terms that we no longer use: relativistic mass, transverse mass (which is identical to relativistic mass), and longitudinal mass.

Yes i know, i am not using the other masses and neither did i come in (serious) contact with them in college (i was just confused how the concept comes into being, without realising it since it doesn't influence any of the calculations i have seen or did). But in my university everyone says "rest mass" - i guess it is just an habbit, or to make it clearer what is meant. I mean, in GR there are more definitions of mass, so i guess it is not that bad idea to use "full name" for them.

Edit: Anyway, thanks again. Let's not lead this thread out of its original topic

 

[Mister T]

I mean, in GR there are more definitions of mass, so i guess it is not that bad idea to use "full name".

In the standard terminology of physics there is only one kind of mass, the ordinary mass. It just causes confusion to call it the rest mass.