What has the speed of light got to do with time travel?

[JesseM]

What happends if you reach the speed of light? Time stops. Of course, this is just silly hypothetical non-reality physics, but everybody loves to think it would. Consequently, ftl travel would logically mean reverse time travel.

If you mean that a clock moving at light speed would be stopped, and therefore that a clock moving faster than light would be running backwards, you're wrong, the Lorentz transformation simply doesn't give a meaningful answer about the rate of ticking of an FTL clock (if you try to apply the Lorentz transformation to an FTL clock, you get the nonsensical answer that the time between its ticks would be an imaginary number). As I've said before, the reason FTL is associated with time travel has nothing to do with FTL clocks or what would be seen by an FTL observer, and everything to do with how FTL signals would look from the perspective of slower-than-light observers; because different slower-than-light frames define simultaneity differently, if you have a signal that moves FTL, it will always be possible to find a frame where the time that a message is received is actually earlier than the time it was sent.

 

[atyy]

Actually, there is an interesting heuristic I've heard. From the "missing" solar neutrinos, it was hypothesized that neutrinos "oscillate". If null-particles don't "experience" time, then they cannot "oscillate". So if neutrinos "oscillate", they cannot be null-particles. I don't know if this language can be turned into something well-defined, since photons obviously oscillate too in some sense.

So it turns out this can actually make some sense.

The absence of neutrino oscillations does not mean that neutrinos have zero mass. However, the existence of neutrino oscillations imply that at least one neutrino has mass. Each neutrino is itself a wave, and the mass difference is the change in relative phase between neutrino waves. What has this got to do with light not "experiencing" time?

The idea that light does not "experience" time can be made sensible in a limited way. For example, light moves relative to us, so we can use the successive peaks and troughs of a light wave moving past us to measure time. In this sense, we "experience" time. However, the speed of light is the same for light of all frequencies, so light does not move relative to light. If two light waves of different frequencies set out in the same direction, any particular peak in one of the waves will not move relative to the nearest peak or trough in the other wave. It will never experience the peaks and troughs of the other wave moving past it. In this sense, a light wave does not "experience" time.

So basically, light not "experiencing" time means that light waves of different frequencies maintain constant relative phase. Furthermore, by analogy to neutrino oscillations, a "photon oscillation" would be a change in relative phase between two light waves of different frequencies. For this to happen, there must be a slight difference in their velocities, and at least one wave cannot travel at the speed of light. Since things that do not travel at the speed of light must have mass, "photon oscillations" would imply that at least one frequency of light is massive.

http://en.wikipedia.org/wiki/Neutrino_oscillation
http://arxiv.org/abs/hep-ph/9905257

 

[WillBlake]

What's your point? Just because logic is a part of philosophy and is also used in science, that doesn't mean all philosophy (including notions of 'cause and effect' which are not part of logic) is part of science too. Just think of it as a Venn diagram with "logic" in the overlap between the circle marked "philosophy" and the circle marked "concepts essential to science".

Without getting too philosophical, science and philosophy are based on the same method of thinking which is an "if, then" system, there is no difference. Science boasts of having "facts" but these are simply agreed upon conjectures and labels which help us deal with reality as we sense it, just like philosophy does. Mysticism is outside these realms.

To provide my viewpoint on the speed of light and time, may I suggest the following: It is easier for me to understand these concepts, if I use the speed of light as the reference point, that is: it is zero and we are currently moving close to the speed of light. This makes sense to me because time is also zero at the speed of light. So to travel back in time, we would have to go less than zero, by this reference point. More interesting, is the question as to why we can't go slower than zero as we conventionally define it? These two limits of speed are the same thing. If we can go slower, we can experience time at a faster rate. I would like to see some math which tackles the question of going slower than zero as we currently define it. This may answer your dilemma. My math is rusty, and I only have a doctorate of philosophy in biotechnology.

 

[JesseM]

To provide my viewpoint on the speed of light and time, may I suggest the following: It is easier for me to understand these concepts, if I use the speed of light as the reference point, that is: it is zero and we are currently moving close to the speed of light. This makes sense to me because time is also zero at the speed of light.

The notion that time dilation approaches infinity as you approach the speed of light only applies to inertial coordinate systems in SR. You can invent a coordinate system where light is at rest and we are moving at c or close to it, but this is not a valid inertial coordinate system in SR, so you can't assume that time dilation in this system works anything like the way it works in inertial frames.

I would like to see some math which tackles the question of going slower than zero as we currently define it.

If you're asking about a speed slower than zero, then I've told you before that this is nonsense because of the very definition of speed. You might as well ask about a number whose absolute value is less than zero, or a square with five corners.

 

[atyy]

To provide my viewpoint on the speed of light and time, may I suggest the following: It is easier for me to understand these concepts, if I use the speed of light as the reference point, that is: it is zero and we are currently moving close to the speed of light.

I am going to speculate a bit here, so I don't know if this is right. I am using "!=" to mean "not equal".

Yes, it is interesting why we cannot set the speed of light to be zero, whereas we can set say 32^oF o be 0^oC. Anyway, it seems that as long as we only add or subtract temperatures, that is not a problem, because 0+5!=0+1 [Eqn 1]. If we do multiply temperatures, as in thermodynamics, then it does matter that we use absolute zero as a reference, not 0^oC, because 0X1=0X5.

Now, we can set the speed of light to be 1, because 1X5!=1X1 [Eqn 2]. Comparing Eqn 1 and Eqn 2, we see that 0 with respect to addition is like 1 with respect to multiplication. So if you want to define the speed of light as zero, it may work if you, for starters, define addition to be multiplication and multiplication to be addition. The mathematicians have thought long and hard about this and they call this "abstract algebra":
http://en.wikipedia.org/wiki/Group_(mathematics )
http://en.wikipedia.org/wiki/Field_(mathematics )
Note particularly in the definition of a field, that "For technical reasons, 1 is required not to equal 0."

You can certainly take the speed of light to be negative, as long as you interchange all positives and negatives in your equations.

The basic idea in the renaming game is that you can rename things anyway you like. One major rule is: you can give two different names to the same thing, but you cannot give two different things the same name. How to play the renaming game in physics is called "gauge theory". Now this game is obviously very confusing, so instead of reading Wikipedia on gauge theory, I recommend:
V Parameswaran Nair, Quantum Field Theory: A Modern Perspective (Springer, 2005)
Xiao-Gang Wen, Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons (OUP 2004)
Peter Olver, Equivalence, Invariants and Symmetry (CUP 1995).
These books don't talk about renaming zero and one, but they talk about renaming 1 to be 3 and 8 to be 9, and zillions of other sorts of renaming.

 

[JesseM]

Yes, it is interesting why we cannot set the speed of light to be zero

You can, but just not if you use an inertial coordinate system.

You can certainly take the speed of light to be negative, as long as you interchange all positives and negatives in your equations.

Not without changing the definition of speed, which is normally defined as the norm of the velocity vector (and the norm of a vector is positive)

 

[atyy]

You can, but just not if you use an inertial coordinate system.

Oooh interesting! How does that work in a non-inertial frame?

Not without changing the definition of speed, which is normally defined as the norm of the velocity vector (and the norm of a vector is positive)

Yes, I should have said velocity. Perhaps we can also reverse the signature convention?

 

[JesseM]

Oooh interesting! How does that work in a non-inertial frame?

You can define a non-inertial coordinate system in pretty much any arbitrary way you dream up. For instance, if we define the coordinates of some inertial frame as x and t, here's a simple coordinate transformation that gives a non-inertial frame where the speed of photons moving in the +x direction will be zero:

x' = x - ct
t' = t

 

[atyy]

You can define a non-inertial coordinate system in pretty much any arbitrary way you dream up. For instance, if we define the coordinates of some inertial frame as x and t, here's a simple coordinate transformation that gives a non-inertial frame where the speed of photons moving in the +x direction will be zero:

x' = x - ct
t' = t

That seems to be somewhat different from setting c=0. It seems to be more about where we set x or t to be 0?

 

[atyy]

You can define a non-inertial coordinate system in pretty much any arbitrary way you dream up. For instance, if we define the coordinates of some inertial frame as x and t, here's a simple coordinate transformation that gives a non-inertial frame where the speed of photons moving in the +x direction will be zero:

x' = x - ct
t' = t

OK, that seems to work.

 

[JesseM]

That seems to be somewhat different from setting c=0.

What do you mean by "setting c=0"? When people talk about setting c=1 they really must mean picking a system of units where c has a value of 1 in those units, but they're still assuming the same kind of inertial coordinate systems where c is the maximum speed. I'm talking about picking a coordinate system where the speed of photons in one direction is zero, regardless of your choice of units.

It seems to be more about where we set x or t to be 0?

Well, it's about the whole coordinate system, not the placement of the origin. In the example I gave, the non-inertial coordinate system's origin coincided with that of the inertial one, but you could also come up with a transformation where the origin x=0,t=0 of the inertial frame corresponded to some other position x'=X,t'=T in the non-inertial one:

x' = x - ct + X
t' = t + T

You can see that the placement of the origin doesn't matter here, it's still true that a photon moving in the +x direction of the inertial frame has a speed of 0 in the non-inertial one.

 

[atyy]

What do you mean by "setting c=0"? When people talk about setting c=1 they really must mean picking a system of units where c has a value of 1 in those units, but they're still assuming the same kind of inertial coordinate systems where c is the maximum speed. I'm talking about picking a coordinate system where the speed of photons in one direction is zero, regardless of your choice of units.

Yes, that's why I didn't understand your proposal right away.

Well, it's about the whole coordinate system, not the placement of the origin. In the example I gave, the non-inertial coordinate system's origin coincided with that of the inertial one, but you could also come up with a transformation where the origin x=0,t=0 of the inertial frame corresponded to some other position x'=X,t'=T in the non-inertial one:

x' = x - ct + X
t' = t + T

You can see that the placement of the origin doesn't matter here, it's still true that a photon moving in the +x direction of the inertial frame has a speed of 0 in the non-inertial one.

Does this have anything to do with black holes?

 

[JesseM]

Does this have anything to do with black holes?

Not that I know of, it's just a different coordinate system to use in flat spacetime, whereas black holes necessarily involve curved spacetime...what made you think of them? I guess the only relationship I can think of is that in GR only local coordinate systems can be inertial ('local' meaning coordinate systems in an arbitrarily small neighborhood of an event, small enough that curvature is negligible), so any coordinate system you use to describe an entire black hole spacetime will be non-inertial, and therefore you can't guarantee that light will still move at c in this system (for example, in Schwarzschild coordinates light rays can actually be frozen at the event horizon, although in the locally inertial coordinate system of a freefalling observer passing right next to the ray as he crosses the horizon, the ray would still be moving at c).

 

[atyy]

Not that I know of, it's just a different coordinate system to use in flat spacetime, whereas black holes necessarily involve curved spacetime...what made you think of them?

for example, in Schwarzschild coordinates light rays can actually be frozen at the event horizon, although in the locally inertial coordinate system of a freefalling observer passing right next to the ray as he crosses the horizon, the ray would still be moving at c

Yes, I was wondering about that. The difference there is between coordinate time and proper time. So similarly for velocities, there is coordinate velocity c_x, and "proper velocity" c (not a standard term). The former can be set any way we want, as long as the transformation preserves the rank of the Jacobian, I think. The latter is a conversion factor between space and time, and I suspect cannot be set to zero because of our choice of notation to describe the field structure of the real numbers. Physically, I'm guessing that we cannot set the conversion factor between space and time, nor the conversion factor between spatial x and spatial y, to be zero because that would be equivalent to reducing spacetime from 4 to 3 dimensional. A second reason must be somehow related to idea that we cannot set the proper time of light to anything except zero.

 

[JesseM]

Yes, I was wondering about that. The difference there is between coordinate time and proper time.

Is it only that, or is there also an issue with coordinate position vs. position as measured in a local inertial coordinate system? I don't know enough about Schwarzschild coordinates to say.

So similarly for velocities, there is coordinate velocity c_x, and "proper velocity" c (not a standard term).

What do you mean by "proper velocity"? Something to do with velocity as measured in local inertial frames? Of course for any object moving slower than light, different local freefalling observers will measure its velocity differently in their own local inertial frame.

The latter is essentially the conversion factor between space and time, and I suspect cannot be set to zero because of our choice of notation to describe the field structure of the real numbers. Physically, I'm guessing that we cannot set the conversion factor between space and time, nor the conversion factor between spatial x and spatial y, to be zero because that would be equivalent to reducing spacetime from 4 to 3 dimensional.

I can't really evaluate what you're saying without knowing how you are defining "proper velocity". As for the conversion factor between space and time, it's the metric which gives you a line element at every point, and that line element tells you how to integrate dt, dx, dy, and dz in your chosen coordinate system in order to get the physical value for the integral of ds along a given path through spacetime (if you're integrating along a timelike worldline, the integral of ds is usually just the proper time converted into a distance). If your coordinate system is an inertial one in flat spacetime, the line element is the familiar ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2, where you're multiplying dt by the "conversion factor" of c before adding it to the spatial increments, but for non-inertial coordinate systems the line element might look completely different. For example, p. 116 of this book mentions that in Schwarzschild coordinates the line element would be:

ds^2 = (1 - \frac{2m}{r}) c^2 dt^2 - \frac{1}{(1 - \frac{2m}{r})} dr^2 - r^2 ( d\theta^2 + r^2 sin^2 \theta d\phi^2 )

So you still have the c^2 factor included in the function you're multiplying dt^2 by (which makes sense since everything is supposed to be in units of distance rather than time), but you're also multiplying by a more complicated function as well.

 

[atyy]

I can't really evaluate what you're saying without knowing how you are defining "proper velocity". As for the conversion factor between space and time, it's the metric which gives you a line element at every point, and that line element tells you how to integrate dt, dx, dy, and dz in your chosen coordinate system in order to get the physical value for the integral of ds along a given path through spacetime (if you're integrating along a timelike worldline, the integral of ds is usually just the proper time converted into a distance). If your coordinate system is an inertial one in flat spacetime, the line element is the familiar ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2, where you're multiplying dt by the "conversion factor" of c before adding it to the spatial increments, but for non-inertial coordinate systems the line element might look completely different. For example, p. 116 of this book mentions that in Schwarzschild coordinates the line element would be:

ds^2 = (1 - \frac{2m}{r}) c^2 dt^2 - \frac{1}{(1 - \frac{2m}{r})} dr^2 - r^2 ( d\theta^2 + r^2 sin^2 \theta d\phi^2 )

So you still have the c^2 factor included in the function you're multiplying dt^2 by (which makes sense since everything is supposed to be in units of distance rather than time), but you're also multiplying by a more complicated function as well.

By "proper velocity" I just meant "c" everywhere in your equations. For example, the non-inertial transformation you first suggested "x'=x-ct, t'=t" doesn't set c=0, it makes the coordinate velocity zero, which is why I was initially confused by your suggestion. I just needed a term to distinguish "c" from the coordinate velocity c_x, and made up "proper velocity" by analogy to "proper time" as an invariant quantity. The line element is some complicated function in general, but I think of "c" as the conversion factor between space and time because it always goes with cdt, no matter how complicated the expression is.

Anyway, to summarize:

1) c_x can be set in any way consistent with a smooth coordinate transfomation, including the nice example you gave

2) c can be set arbitarily to anything except 0, because (this is the speculative part):

-our notation of the field structure of the real numbers defines 0 as the identity under addition, and 1 as the identity under multiplication, so setting c to 0 is not a problem if we only did addition, but it is a problem if we do multiplication because multiplying by 0 gives different things the same name.

-c is the conversion factor between space and time, if you set it to zero, you will be reducing spacetime form 4 to 3 dimensions. However, this cannot be the complete reason, because we can always use some other velocity to do the conversion.

-the proper time of light must be zero, and this corresponds to c being non-zero.

 

[JesseM]

I think you're making this over-complicated...if we're just talking about unit conversions rather than coordinate transformations, no sensible unit conversion will make any quantity which is nonzero in one system of units be zero in the other (unless we're measuring something where by convention we allow the value to be negative or positive, like temperature in degrees celsius). For example, if I used a crazy system of distance units called "kookoos" with the conversion 1 meter = 0 kookoos, that would mean that any finite number of meters would be 0 kookoos, and any finite number of kookoos would be an infinite number of meters--not a very useful set of units for measuring distances in the real world! And this point about unit conversions applies regardless of whether what I'm measuring is the speed of light, or the speed of a car in some particular frame, or the distance from New York to Los Angeles, or my own weight.

 

[atyy]

I think you're making this over-complicated...if we're just talking about unit conversions rather than coordinate transformations, no sensible unit conversion will make any quantity which is nonzero in one system of units be zero in the other (unless we're measuring something where by convention we allow the value to be negative or positive, like temperature in degrees celsius). For example, if I used a crazy system of distance units called "kookoos" with the conversion 1 meter = 0 kookoos, that would mean that any finite number of meters would be 0 kookoos, and any finite number of kookoos would be an infinite number of meters--not a very useful set of units for measuring distances in the real world! And this point about unit conversions applies regardless of whether what I'm measuring is the speed of light, or the speed of a car in some particular frame, or the distance from New York to Los Angeles, or my own weight.

I'd quite happily set my weight to 0.

 

[WillBlake]

The notion that time dilation approaches infinity as you approach the speed of light only applies to inertial coordinate systems in SR. You can invent a coordinate system where light is at rest and we are moving at c or close to it, but this is not a valid inertial coordinate system in SR, so you can't assume that time dilation in this system works anything like the way it works in inertial frames.

If you're asking about a speed slower than zero, then I've told you before that this is nonsense because of the very definition of speed. You might as well ask about a number whose absolute value is less than zero, or a square with five corners.

If I understand this statement correctly, we do not have an appropriate system to set the speed of light to zero. Is this an insurmountable problem? If so, it is too bad, because I feel it would serve as a better method for measuring reality. Moment to moment, time is zero, its passage is just an illusion due to our speed (or is it velocity? :-)).

 

[sanman]

Hi guys, I am responding to comments on the train thought experiment from the first page of this thread. Hope I'm not derailing the conversation. (inadvertent pun)

Anyway, just because one were to propagate information about an event FTL, that doesn't mean one is violating causality, because the propagation of that event would still be happening after the fact of that event. I think Hawking himself made comments to this effect, a few years back. As long as you accept that what you are seeing has already happened before you observed it, then "time travel" is really reduced to "time dilation/contraction".

But one thing that's always bothered me is the question of why the speed of light is always the same to every observer, regardless of reference frame velocity.
How is it possible for light to exhibit this characteristic?
What is the underlying reason for it?

And of course, why does the speed of light have the particular value it has? (ie. 3x10^8 m/s)
What were to happen if it were twice that speed, or two-thirds that speed?
What would be the consequences? How would our universe change?

 

[Fredrik]

Anyway, just because one were to propagate information about an event FTL, that doesn't mean one is violating causality, because the propagation of that event would still be happening after the fact of that event.

See my post in this thread.

But one thing that's always bothered me is the question of why the speed of light is always the same to every observer, regardless of reference frame velocity.
How is it possible for light to exhibit this characteristic?
What is the underlying reason for it?

First of all, you shouldn't think of it as a property of light. The existence of inertial frames and the fact that a certain type of straight line looks the same in all of them is a property of spacetime, not a property of light.

Light does however have the property that it moves at the speed that's associated with the "straight lines" mentioned above. It has to, because photons are massless particles. This is one of the things you find when you combine quantum mechanics with special relativity.

And of course, why does the speed of light have the particular value it has? (ie. 3x10^8 m/s)

No one knows.

 

[cybersurf88]

Ok, I take it you'll be first in line to volunteer for the quantum transporter?


Two reasons: 1) signaling is not travel; 2) MWI avoids causality paradoxes.

How do you view Dr. Gisin's entangled twin photon experiment in FTL signaling and its
implications on practical informational systems. Is the instantaneous twin aberrational
behavior of light photons "merely" explained by random behavior and unpredictability
states and conditions within quantum mechanics? Can signaling become informational?
...

nb. Thank you JesseM for your extraordinarily insightful understanding and explanation.

SEE:
"Entangled particles are identical entities that share common origins and properties, and remain in instantaneous touch with each other, no matter how wide the gap between them..."

"... "collapse of the wave function." ...is that if just one particle in an entangled pair is measured, the wave function of both particles collapses into a definite state that is the same for both partners, even separated by great distances. "
http://www.cebaf.gov/news/internet/1997/spooky.html Jefferson Lab

 

[JesseM]

How do you view Dr. Gisin's entangled twin photon experiment in FTL signaling and its
implications on practical informational systems. Is the instantaneous twin aberrational
behavior of light photons "merely" explained by random behavior and unpredictability
states and conditions within quantum mechanics? Can signaling become informational?

Gisin's experiment does not involve "signaling", only the correlations characteristic of entanglement, but there is no way to use these correlations to gain any information on what measurement was performed on the other distant particle before a classical signal about the measurement has had time to reach you. It has apparently been proven that according to orthodox quantum theory, there is absolutely no way to use entanglement to send FTL signals--there is a theorem by Phillippe Eberhard to this effect, see here. Depending on your choice of interpretation of QM, you may believe there are some "hidden" FTL effects needed to explain the correlations seen in entanglement, but as peter0302 said, advocates of the many-worlds interpretation do often argue that the MWI can explain these correlations without the need for even hidden FTL effects.

 

[cybersurf88]

Thank you. Apparently my question was not precise. I am aware that instantaneous
identical behavior of entangled light photons over long distances did not evidence
FTL informational transmission between the twin photons or any evidence of signaling between the entangled photons.

However, I will rephrase the question as:
Whether the behavioral characteristics of entangled LP can or will present itself as a paradigm for FTL informational systems?

Although the concept of causality in physics is distinct from philosophical causality or legal causality in tort (negligence) cases, I draw from analytic (linguistic-Wittgenstein) philosophy to define causation as being the direct or proximate cause (substantially contributing factor) which resulted in a particular action. As you noted, information can theoretically arrive faster than it is sent. Could instantaneous identical behavioral changes by entangled photons infer that each of the twin photons receive programming instructions independently from another common FTL broadcasting source?

Would the common broadcasting source be a direct or proximate cause of the twin
LP changes over long distances.

This issue is distinct from the proven hypothesis that LP do not communicate between each other.

Do the equations and explanations of long distance - instantaneous twin LP changes
limit our understanding to "aberrant, unexplainable" conditions that fall within quantum physics and quantum mechanics?

What equational inquiries would rule out direct or proximate causation of twin LP
changes by a separate common broadcasting source?

If empirical evidence cannot rule out a common FTL broadcasting source, can
a theory of a single broadcasting source or "collective- but separate broadcasting
sources" be constructed that proves a necessity for the existence of a "broadcasting source for entangled LP?

Instantaneous LP character changes over long distances without an "instructional source" is illogical. It's "spooky quantum mechanics."

Keep in mind Dale's comment to Flash, "...Flash, you'll be traveling so fast that you'll arrive before leaving..."

Anyway, you guys are a hell-a-va lot smarter than me in this area.
So...can I respectfully ask if anyone in this forum is affiliated with university research or teaching. What are the educational backgrounds of the contributors in this forum? The quality and calibre of the discussions is impressive.

I will give my background to anyone who is interested.
Be good, take care all.

 

[Max™]

Light is measured to have a constant velocity even when you're moving rapidly because of the time dilation you incur as you move faster.If you move fast enough that your subjective second corresponds to 1.5 seconds for a beam of light, then you would measure a beam of light crossing 1.5x light-seconds

You yourself would have crossed .5 light-seconds.

So you "see" a second, measure the motion of the light for "a second", move half a light-second, and the beam of light moves 1.5 light seconds.That is why the speed of light is always measured to be constant, and why it is invoked in SR. Not as a statement about the speed of light at all.

Rather as a statement about how motion through space affects motion through time.

 

[JesseM]

Light is measured to have a constant velocity even when you're moving rapidly because of the time dilation you incur as you move faster.

There is no objective truth about who is "moving rapidly" though. If you and I are moving at 0.8c relative to one another, then in my frame I am at rest and you are moving at 0.8c, and your clock is slowed down by a factor of 0.6 relative to mine. Likewise, in your frame you are at rest and I am moving at 0.8c, and my clock is slowed down by a factor of 0.6 relative to yours. There's no real fact of the matter of which of us is "really" moving faster or which of our clocks is "really" running slower.

Also, the fact that each observer measures the speed of light to be c can't be explained solely by time dilation, you also need to take into account length contraction since speed is defined in terms of distance/time, and you need to take into account the relativity of simultaneity (the fact that each observer sees the other one's clocks being out-of-sync). See my post #6 on this thread for a numerical example of how all these factors come together to ensure that both observers measure a photon to move at c.

If you move fast enough that your subjective second corresponds to 1.5 seconds for a beam of light

What do you mean "for a beam of light"? The light does not have its own frame.

then you would measure a beam of light crossing 1.5x light-seconds

If in your frame a light beam travels for 1.5 seconds, then in your frame it will have moved 1.5 light-seconds--is that what you mean?

You yourself would have crossed .5 light-seconds.

0.5 light-seconds in whose frame? In the frame of the observer who sees your clock take 1.5 seconds to tick forward one second? If so, your numbers are incorrect, in order to have gamma = 1.5 in my frame, your velocity must be approximately 0.745346c in my frame, so in 1.5 seconds I'd see you travel 1.5*0.745346 = 1.11803 light-seconds.

 

[Max™]

Why does the beam of light not have it's own frame?

What would an event look like for a beam of light, if it was an observer?

They're weird questions which aren't normally approached.Yes I did neglect the length contraction for simplicity, it all applies and should be calculated to be accurate, but the point is that the measured speed of light being constant is a statement about the way we interact with space-time, not the speed of light itself.

Light interacts with space-time in a different manner, for it has no rest mass.Naturally this will all be observed differently for an observer in a different frame of motion.

I apologize because I too naturally include GR assumptions about acceleration and reference frames, but to be fair, SR is not truly complete without GR.

 

[JesseM]

Why does the beam of light not have it's own frame?

What would an event look like for a beam of light, if it was an observer?

This is a question which has been discussed on many previous threads here. Here was my brief explanation in one older thread:

Inertial frames are supposed to be defined by networks of rulers and synchronized clocks at rest in that frame, but it's impossible for rulers and clocks to be accelerated to the speed of light, and even if you consider the limit as they approach the speed of light, the rulers' length would approach zero due to Lorentz contraction and the clocks would approach being completely frozen due to time dilation, so you couldn't construct a sensible coordinate system out of them. One more reason that light can't have its own inertial rest frame is that one of the fundamental postulates of relativity is that the laws of physics should be the same in every inertial frame, but light can never be at rest in the rest frame of any object moving slower than light, so giving light its own rest frame would violate this postulate.

For more on the subject of light not having its own frame, you might look at this thread or this one.

Yes I did neglect the length contraction for simplicity, it all applies and should be calculated to be accurate, but the point is that the measured speed of light being constant is a statement about the way we interact with space-time, not the speed of light itself.

What do you mean by "the speed of light itself"? Do you think objects have a true speed which is separate from the distance/time measured by various sets of rulers and clocks?

I apologize because I too naturally include GR assumptions about acceleration and reference frames, but to be fair, SR is not truly complete without GR.

SR is complete as long as you are dealing with a situation where spacetime is not curved (just assume the mass of all the particles is negligible). You can certainly deal with acceleration in SR, see here.

 

[cybersurf88]

...ask if anyone in this forum is affiliated with university research or teaching. What are the educational backgrounds of the contributors in this forum?

Can anyone link me to abstracts on FTL communication...?

 

[Max™]

For a photon, a point in space directly corresponds to a point in time.

Photons move through time in a way which is equivalent to motion through space.

Yesterday for a photon is "over there", tomorrow is "that way", now is "right here".

We (bodies with rest mass) move through time at a much reduced rate. Having a rest mass, or sitting still in an inertial frame, can be considered motion at a sub-light velocity from another frame.

If you're moving through space at a sub-light velocity, you are falling behind the time marked out by a photon. You observe this as time dilation.If a photon passes you at "now", and you take off at, say, twice the speed of light in the same direction. When the photon crosses a light minute (1 minute later from the "now" it passed you), you're 1 light minute ahead of it.

You then turn around and go past the point where the photon crossed you, but you are "ahead" of it. The photon is actually further back along it's path than it was when it first passed you.

You crossed that "now" before the photon did, because you went back in time along a closed timelike curve.These ideas seem weird until you consider what the universe looks like to a photon.

That is similar to what Godel was doing when he constructed his Godel Universe.