From what popular science tells us, if I travel at close to the speed of light, I'd age slower. So if I travel at 99% of SOL and travel the distance of one light year, for other people one year has passed. But for me, hardly any time has passed.

So - for me and my ship, we travelled one light year in very little time. If that is the case, then for me I travelled much faster than the speed of light!

How does that reconcile with the statement that nothing can exceed the speed of light?

You have neglected length contraction in your analysis. You see the initial distance of the star contracted by the same factor that the elapsed time is shortened.

So, from the perspective of the Earth, you take 1.0101 years to travel a distance of 1 light year at a speed of $0.99c$.

From your perspective, the destination comes to you. It arrives after 0.1425 years, travelling a distance of 0.1411 light years, again at a speed of $0.99c$.

No faster-than-light travel is involved anywhere.

(In the above, I have rounded non-terminating decimals to 4 decimal places)

## How Faster than Light Speed Breaks CAUSALITY and creates Paradoxes

**How Faster than Light Speed Breaks CAUSALITY and creates Paradoxes**

2:43 – Why is there a speed limit?

6:22 – What if speed of light was infinite?

8:29 – What if we could send instantaneous subspace signals?

14:12 – Special offer from Wondrium

**Summary:**

If you point a powerful laser at the moon, and spin it 100 times per second, the dot on the moon will move 3X the speed of light. This is ok. The maximum speed limit is not a limit with which things can move, but is a limit on the speed of causality. A cause cannot have an effect anywhere in the universe faster than the speed of light.

But what are the implications of having a speed limit on causality. Why is there a limit in the first place? And how would causality be broken if information could travel faster than light.

Only a force can cause something. The speed of information is the speed of a force field. You can’t send information faster than the force field can change. This sets an upper limit on its speed. Light in a vacuum travels at c, the maximum speed because photons are massless. Without mass there is no restriction on their velocity.

Einstein’s theory of special relativity is based on two postulates. Neither of the postulates state that nothing can travel faster than light. The first postulate is that the laws of physics are the same in every reference frame. The second postulate states that the speed of light in a vacuum is constant, and independent of the motion of the source of that light.

But what if this maximum speed was infinite, implying that the speed of light is infinite? For one thing using the equation E=MC^2, it would require an infinite amount of energy to accumulate any mass in the universe. So no massive particles could form.

The other problem is that we would not have light at all. In Maxwell’s equations. c equals one over the square root of the permittivity and permeability of free space. Permittivity is the resistance of free space to the formation of electric fields, and permeability is the formation of a magnetic field by an electric current. But if you set c equal to infinity, it would mean that these interactions of electricity and magnetism would not happen. There would be no waves, and thus, no light.

#fasterthanlight

#causality

What if we kept special relativity, but we allowed faster than light communication, for example like instant subspace communication like in Star Trek? The problem is that in special relativity, it is not clear what instantaneous means. What’s happening “right now” depends on how fast, and in which direction you’re moving. There is no absolute now. The now depends on the reference frame.

For example, imagine Alice on earth, and Bob in a rocket traveling 0.87c towards Proxima Centauri, our nearest neighboring star.

The world line for Alice will be straight up, because she will not be moving in her frame of reference, but she will be moving forward in time. Her clock on her world line will tick normally for her. Bob&rsquos clock will be moving at half the rate of Alice&rsquos due to Bob&rsquos speed relative to Alice

But from Bob’s perspective, he is not moving, and the earth is moving away from him at 0.87c. So from Bob&rsquos perspective his clock is running normally. And it is Alice’s clock that is running at ½ the speed of Bob’s clock.

Here&rsquos how this would break causality: Alice sends a message to Bob using an instantaneous signal to Bob at her 4 seconds. It would arrive to Bob when his clock reads 2 seconds. But from Bob’s perspective, Bob receives the signal at 2 seconds, when Alice’s clock was at 4 seconds. But her clock is running slower than Bob’s from Bob’s perspective. This means that the signal from Alice would have to travel back in time to reach Bob.

Because Bob receives the signal at 2 seconds, he could read the signal and reply at his 4 seconds using the same instantaneous « subspace » signal. That means Alice would receive the reply at her 2 seconds. She would receive the reply BEFORE she sent the message at 4 seconds.

If this was permissible, Alice could use Bob to send messages to herself in the past. She could send a message to herself at 2 seconds, to not the send the message to BOB at 4 seconds. In that case, how did she receive a reply to a message that she never sent?

Anything that allows information to travel to the past causes paradoxes like this and the grandfather paradox, among others. So such a thing is not permissible, and does not happen according to physics as we understand it. There is no absolute time. And there is no absolute now.

## Spacecraft in a ‘warp bubble’ could travel faster than light, claims physicist

Albert Einstein’s special theory of relativity famously dictates that no known object can travel faster than the speed of light in vacuum, which is 299,792 km/s. This speed limit makes it unlikely that humans will ever be able to send spacecraft to explore beyond our local area of the Milky Way.

However, new research by Erik Lentz at the University of Göttingen suggests a way beyond this limit. The catch is that his scheme requires vast amounts of energy and it may not be able to propel a spacecraft.

Lentz proposes that conventional energy sources could be capable of arranging the structure of space–time in the form of a soliton – a robust singular wave. This soliton would act like a “warp bubble’”, contracting space in front of it and expanding space behind. Unlike objects within space–time, space–time itself can bend, expand or warp at any speed. Therefore, a spacecraft contained in a hyperfast bubble could arrive at its destination faster than light would in normal space without breaking any physical laws, even Einstein’s cosmic speed limit.

### Negative energy

The idea of creating warp bubbles is not new, it was first proposed in 1994 by the Mexican physicist Miguel Alcubierre who dubbed them “warp drives” in homage to the sci-fi series *Star Trek*. However, until Lentz’s research it was thought that the only way to produce a warp drive was by generating vast amounts of negative energy – perhaps by using some sort of undiscovered exotic matter or by the manipulation of dark energy. To get around this problem, Lentz constructed an unexplored geometric structure of space–time to derive a new family of solutions to Einstein’s general relativity equations called positive-energy solitons.

Though Lentz’s solitons appear to conform to Einstein’s general theory of relativity and remove the need to create negative energy, space agencies will not be building warp drives any time soon, if ever. Part of the reason is that Lentz’s positive-energy warp drive requires a huge amount of energy. A 100 m radius spacecraft would require the energy equivalent to “hundreds of times of the mass of the planet Jupiter”, according to Lentz. He adds that to be practical, this requirement would have to be reduced by about 30 orders of magnitude to be on par with the output of a modern nuclear fission reactor. Lentz is currently exploring existing energy-saving schemes to see if the energy required can be reduced to a practical level.

Any warp drive would also need to overcome several other serious issues. Alcubierre, who regards Lentz’s work as a “significant development”, cites the “horizon problem” as one of the most pernicious. “A warp bubble travelling faster than light cannot be created from inside the bubble, as the leading edge of the bubble would be beyond the reach of a spaceship sitting at its centre,” he explains. “The problem is that you need energy to deform space all the way to the very edge of the bubble, and the ship simply can’t put it there.”

### Spacecraft doubts

Lentz describes his calculations in *Classical and Quantum Gravity*, where other recent research on the topic is outlined in an accepted manuscript from Advanced Propulsion Laboratory researchers Alexey Bobrick and Gianni Martire. The duo describes a general model for a warp drive incorporating all existing positive-energy and negative-energy warp drive schemes, except Lentz’s which they say “likely forms a new class of warp drive space–times”.

However, they argue that a Lentz-type warp drive is like any other type of warp drive in the sense that, at its core, it is a shell of regular material and therefore subject to Einstein’s cosmic speed limit, concluding that “there is no known way of accelerating a warp drive beyond the speed of light”.

Though he recognizes these huge hurdles to building a warp drive, Lentz feels they are not insurmountable. “This work has moved the problem of faster-than-light travel one step away from theoretical research in fundamental physics and closer to engineering,” he says.

After addressing energy requirements, Lentz plans to “devise a means of creating and accelerating (and dissipating and decelerating) the positive-energy solitons from their constituent matter sources”, then confirm the existence of small and slow solitons in a laboratory, and finally address the horizon problem. “This will be important to passing the speed of light with a fully autonomous soliton,” he says.

**Benjamin Skuse** is a science writer based in Somerset, UK

## Faster than Light Particles?

A meeting at Cern, the world’s largest physics lab, has addressed results that suggest subatomic particles have gone faster than the speed of light.

This could be big! News from CERN, the European Organization for Nuclear Research have created what seem to be neutrinos traveling faster than light. Its too early to get too excited, but if it turns out to be right, it will shake up one of the pillars of modern physics, Einstein’s relativity! It is likely to be some kind of unaccounted for process or systematic error in the experiment, but it may not be. A good scientist will remain skeptical until all other possible explanations are ruled out.

If these measurements turn out to be right, and if it turns out that some physics has to be rebuilt from the foundation, it will be an exciting time for young physicists. Any time there has to be a reconstruction at the foundations of physics is a fun time to be working physicist. Sting Theory has consumed many theoretical physics careers in the last couple decades, but this would give new minds something of major importance to work on…and likely win some Nobel Prizes in the effort. Who wants to be the next Einstein, Bohr or Heisenberg? Any takers? Go out and earn those PhD.s in physics and go get it!

### Share this:

## Faster than light travel

I know, it violates the laws of physics. Can't possibly be done.

Then there's the arguement "but the laws of physics also used to say the Earth was flat, etc etc", and the counter-arguement "but that was before the introduction of the scientific method, etc etc".

Let's get past all that. I firmly believe that practical interstellar travel is possible without resorting to multigenerational vehicles. We just haven't found the breakthrough principle and technology yet. That's the nature of revolutionary discoveries: they change everything.

Is there any real reason to think that such a discovery is actually, truly impossible? OK, genuine FTL travel in normal space may be impossible but that may not be the only way to approach it. Wormholes, interdimensional jump, etc: who's to say that some bold new idea and invention (e.g the Infinite Improbability Drive) couldn't harness these possibilities?

Without resorting to "That's ridiculous, it's impossible" at one extreme, and "Ahead warp factor one" at the other, could there be such a discovery coming sometime? Could others in the galaxy already be using it? Let's have some open minds here (without any brains falling out). There are some really smart people here what do you think?

### #2 llanitedave

Well, there's the intruiging fact of quantum entanglement, which looks very much like instantaneous information (but may not be in actuality), and there's the idea that expanding space can drag galaxies along with it at faster than light speeds relative to even more distant galaxies, so

As long as you aren't moving through space, the speed limit may not apply. Now all you have to do is figure out a way to get somewhere without moving through space.

### #3 VictorB

As i know by studing it, light is a particle but also a wave. Space is not completly empty and scitifics know that. Black matter affects the light by making it drift. And if the balck Matter was kind of an mini obstacle to the light? Like in the water, light travel less faster. If there is a gap in the universe that contain no matter, light will travel maybe twice faster.

Ok i know im crazy but who knows. it's just an hypotesis. its actually good too have some creativity when you want to be a astrophysicist

### #4 MMICKELS

Looks like some folks have thought about how to do it. As far as some folks in our galaxy doing the same, I suppose it's possible if there are some folks out there. I would think that even if you could travel at twice the speed of light, you would need to use some sort of suspended animation to keep the needed amount of food, water and air down to a minimum.

### #5 saxmaneagle

. and I too share Rick's line of thought.

### #6 jayscheuerle

The energy requirements to accelerate even subatomic particles even close to light-speed is enormous.

My numbers here are no doubt wrong, but the sense it conveys is correct: I once read that in order to accelerate something the size of a subcompact car to 90% of the speed of light would take the energy equivalent of 200,000 atomic bombs the size of which were dropped over Hiroshima.

Then you'd need that much to stop.

- and the laws of physics never said Earth was flat. That was just a rational observation that turned out to be wrong.

In the end FTL travel is all about energy. - j

### #7 deSitter

Relativistic invariance may be different on either a small or huge level - but in the world we inhabit every day, it's an ironclad rule.

Actually if you can get going fast enough, you can go anywhere you want in as little time as needed, since time compression will shorten your journey - e.g. you can get to Andromeda in a few days, and get back in a few days, assuming you have enough energy to burn. Unfortunately millions of years will have passed on Earth. So the restrictions on space travel are social, not physical. Those who go are on their own. What they discover cannot have any effect on social systems as we understand them.

There is one hope, a slim one - let's say matter and spacetime are related and time has more than 1 dimension - let's say 3. Matter could be "converted" into spacetime and converted back at "some other place". You'd be side-stepping relativistic invariance. The process would be something like "beaming up". Basically, the arrow of time could rotate out of its former fixed direction and then rotate back "later" and "elsewhere". That could happen if the basic "invariance group" of physics was larger than that which underlies relativity. The process described could be thought of as a generalization of matter-antimatter creation and annihilation. If you think about it, when a pair is created from the vacuum, they got there without being anywhere else first. Having a multi-dimensional time allows a distinction between persistence (whether or not something exists) and duration (how long it exists measured with respect to the arrow of time).

Now the alternatives to this are practically non-existent. There has to be SOME group that organizes physical law, and it has to have the relativity group as a sub-group - meaning, it has to have either extra space or extra time dimensions. Cogent reasons say, they can't be space-like (we'd see them, we'd be unable to tie our shoes). But extra time-like dimensions are definitely possible. You can use them to create a unification of gravity and electromagnetism, or really any Yang-Mills field.

## Faster-than-light travel discovered? Slow down, folks

So the web is buzzing right now over news that scientists have detected some subatomic particles moving faster than the speed of light.

Yeah, well, not so fast. Let’s think about this for a sec.

First, what happened is that they create these particles, called neutrinos, at CERN in Geneva. Neutrinos don’t interact with normal matter well, so they can pass right through the Earth as if it isn’t there. In a fraction of a second, some of them enter a detector called OPERA in Italy where they are recorded (pictured here). If you divide the distance between those two points by the time it takes for the neutrinos to travel, you get their speed.

And when the scientists did that, they find the neutrinos get to Italy about 60 nanoseconds faster than a photon would.

Photons travel at the speed of light – they *are* light! – so this means the neutrinos, if this is all true, traveled faster than light speed. Holy Kessel Run!

Now first off, if it were this would overturn so much physics that they may as well have discovered that gravity pushes, not pulls. So right away we need to treat this claim with lots and lots of skepticism. I’ll note these are actual particle physicists making this claim, and not some crackpots who will shake their fists at the sky and say how Galileo was laughed at too.

The thing to do is to look at where this claim might have gone awry. First, the timing is interesting. They claim a measuring accuracy of 10 nanoseconds, so 60 ns would be pretty significant. However, my first thought is that light travels about 30 centimeters in 1 ns, so they need to know the distance between the source and the detector to an accuracy of 3 meters. If they are off by 20 meters, then we’re done that would explain the difference entirely. I suppose this depends on how they measured the distance and the speed of the particles, too. However, they haven’t published a paper on this just yet, so that’ll have to wait.

*[UPDATE: The paper is now up on the arxiv preprint server. I took a look, and must say at first glance their reasoning looks solid. They appear to have the baseline distance nailed and the timing as well. However, the devil’s in the details, and this isn’t my field, so I’ll be very curious to see how the pros in this discipline react to the paper.]*

Also, as pointed out in a Science Magazine article, knowing the exact moment the neutrinos are created isn’t easy either. Mind you, 60 nanoseconds is 0.00000006 seconds, so they need a pretty good clock here. That page also says they used GPS to determine the distance, which *could* be off a bit.

There’s another point that actually is quite important here. If neutrinos travel faster than light, then we should’ve detected the neutrinos from Supernova 1987A *before* we saw the explosion itself. That exploding star was formed when the core of a massive star collapsed, detonating the outer layers. The collapsing core blasted out a furious wave of neutrinos strong enough to be seen here on Earth, over 160,000 light years away.

The distance from the detector in Italy to the source in Geneva is about 730 km. The travel time at the speed of light is about 2.43 milliseconds, and the neutrinos appear to have outraced that speed by 60 nanoseconds. If true, that means they were traveling just a scosh faster than light, by about 1 part in 40,000. The neutrinos from SN1987A traveled so far that had they been moving that much faster than light, they would’ve arrived here *almost four years before the light did*. However, we saw the light from the supernova at roughly the same time as the neutrinos (actually the light did get here later, but it takes a little while for the explosion to eat its way out of the star’s core to its surface, and that delay completely accounts for the lag seen).

But I wouldn’t use that argument too strongly perhaps this experiment creates neutrinos in a different way, or the neutrinos from this new experiment have different energies than ones created in the cores of supernovae (a good bet). Still, it’s enough to make me even more skeptical of this FTL claim.

I’ll note that the scientists will be presenting these results tomorrow at a conference at CERN. We’ll learn more then. It’s not clear to me if these results are being published, or have been peer-reviewed, or what. As usual, we’ll need to have other scientists either confirm this result using other equipment, or show where things went wrong. That’s how science works. And the scientists involved are asking for criticism here! That’s just so incredible results need to be tested incredibly well.

So don’t let your imagination run away with this just yet. This result will, in my opinion, probably turn out to be incorrect for some reasons dealing with measurement. Faster than light travel is still a dream, even though I wouldn’t say it’s impossible… just very, very, very, very unlikely.

Maybe someday we’ll boldly go. But for now, I’m not betting my dilithium on it.

## The fun of going faster-than-light

Well as we now know from the "Thinking in 4d" thread ( ) that contraction stuff doesn't happen that-a-way - and the SOL is not anything about light itself, rather, a characteristic of the geometry which happens to have the dimensions of a speed, because the geometry relates time to space - this speed is either finite, or not, and the only way to know which, is to look - and when you look, it's finite. That light goes at the maximum speed is a consequence of it being a massless field. Equivalently - things that go at the maximum speed, cannot go less, or more - they always go at the maximum speed.

Things cannot go faster than this speed because they lose causal contact not only with the rest of the universe, but with each other. So pinkelephantons may be zipping past your ears right at this moment, but you'll never know, and your instruments will never know, because they cannot possibly interact with real elephants, or you. It is therefore pointless to speak of things going faster than the maximum speed, because they cannot be detected, even in principle.

It's a shame Feynman made this wrong remark, but teaching relativity was not his strong point.

I hate to poop the party, but this sort of thing is not fun - it's not only wrong in principle, it obfuscates the reality of relativity. There is no imaginary mass - the imaginary unit "i" of algebra has a very definite meaning, and mass is not it. Strangely enough, this meaning comes from Euclidean, not Lorentzian, geometry, and basically, it's "infinity" in its most primitive geometric clothes.

### #3 Shadowalker

Things cannot go faster than this speed because they lose causal contact

I suppose if something were undetectable because something must *cause* an effect to be measured, for practical purposes it doesn't exist.

But we do have a tool to analyze - mathematics works for causal and non-causal systems. Back in engineering school my eyes glazed over when we discussed non-causal systems. If it wasn't real I wasn't interested. Later, I learned that the math that described them was still useful. The two-sided Fourier transform, for example, relies on *future* values of input. Take the inverse, and you start to get a response *before* the input is applied. Seemed like magic to me.

Turns out the math is still useful and alows one to do things with *recorded* data that you can't do with real-time data. Obviously, these processes are not really non-causal, but it uses the same math, and the systems behave as the math predicted.

So can we deduce from math that certain things exist with any certainty? The kind of certainty we'd have if they were causal?

### #4 Bob Andersson

And, as we all know, the speed of light limitation only applies to those **not** inhabiting one's personal rocket. Give me a spaceship with the oomph to accelerate at a constant 1G for ever and I can get almost anywhere in a reasonably quick time. It's just those poor unfortunates left behind who age and die far too fast.

### #5 Wes Tausend

Well as we now know from the "Thinking in 4d" thread ( ) that contraction stuff doesn't happen that-a-way - and the SOL is not anything about light itself, rather, a characteristic of the geometry which happens to have the dimensions of a speed, because the geometry relates time to space - this speed is either finite, or not, and the only way to know which, is to look - and when you look, it's finite. That light goes at the maximum speed is a consequence of it being a massless field. Equivalently - things that go at the maximum speed, cannot go less, or more - they always go at the maximum speed.

Things cannot go faster than this speed because they lose causal contact not only with the rest of the universe, but with each other. So pinkelephantons may be zipping past your ears right at this moment, but you'll never know, and your instruments will never know, because they cannot possibly interact with real elephants, or you. It is therefore pointless to speak of things going faster than the maximum speed, because they cannot be detected, even in principle.

It's a shame Feynman made this wrong remark, but teaching relativity was not his strong point.

I hate to poop the party, but this sort of thing is not fun - it's not only wrong in principle, it obfuscates the reality of relativity. There is no imaginary mass - the imaginary unit "i" of algebra has a very definite meaning, and mass is not it. Strangely enough, this meaning comes from Euclidean, not Lorentzian, geometry, and basically, it's "infinity" in its most primitive geometric clothes.

I don't think everyone will be happy with what I am about to say. Perhaps now, I will find out what was meant by "Welcome to the Wars", in the "Thinking in 4d" thread.

I agree with deSitter for much of his post above. Except the statement, *"Well as we now know from the "Thinking in 4d" thread ( ) that contraction stuff doesn't happen that-a-way. "*.

Actually, I believe that the ball shown in the diagram.

. foreshortens exactly as depicted.

(Image credit: Universe Review.)

There are multiple truths involved.

The confusion arises in that we cannot use the "relatively slow speed of light" to instantly see it foreshortened that way. The ball must indeed flatten perpendicular to the direction of travel as is shown, but we could not detect it in any normal sense, and the ball would appear round only **as viewed**, using light as a medium. The reason this point is important, is that we sometimes really view astronomical objects that are "abberated" by the "near velocity C" visual effect. To quote from my former "Thinking in 4D" post, *"There are some wonderful practical revelations in the effect, especially in answering apparent superluminal observations of quasars."*

The distorted visual effect, as I understand it, is similar to an imaginary scenario involving sound. I know sound and light energies can not be directly compared, but there are simularities and analogies in the form of thought experiments.

Imagine that you are riding in a slow Piper Cub one fine serene day. Only 1000 feet ahead of you, slightly off to one side, is your best friend, riding in another slow Piper Cub. Your friend decides to pull a joke on you and throws a lit firecracker out of his door, directly in front of your path. Traveling behind him, you will hear the firecracker explode, almost in a normal sense. You may note a slight doppler effect, but not consider the effect extraordinary to the extreme.

But now imagine your friend is in the same Piper Cub, and you are in a fast jet about to pass him at Mach II. He sees you approaching quickly and, again, throws a fire cracker out the door to surprise you, directly in front of your path. Since your velocity is twice the speed of sound, but less than that of light, you will see the flash from the exploding firecracker, but you will not hear it in any normal sense. You will actually nearly pass through the firecracker burst before the soundwave can possibly get to you nomally, because of the extreme timing. (If the firecracker were off to one side, you might pass by the soundwave before you could hear it at all, and it would never catch you.) Yet the sound directly in your path will affect your sense of hearing in a very distorted way. I believe a similar sense-limited "timing" effect, concerning light distortion, is explored in the "Thinking in 4D" thread. A very fast, blind bat might regard the sound barrier very much as we regard the light barrier. But are they really barriers, or just perceptive limits, in the grand scheme of things? I think light is a "real" barrier, but I have a slightly different take on it.

And, of course, in the end, your friend will be really, really surprised from the effects of you passing within inches of his flimsy Piper Cub wing at Mach II. Boom!

Let us consider that during the linked 4D effects, of the "Thinking in 4D" thread, the soccer ball and the "slowed light" video struggle to demonstrate 4 dimensional perspective. I should point out, that nowhere within the first http://www.spacetimetravel.org/ links, nor in the above "slowed light" video, are outright direct claims made, in so many words, that these computer animations support full 4 dimensional comprehension or realisation of such. Coincidentally, the words "4 dimension" are simply not used. The words "Relativity visualized", or "allows us to see special relativistic effects" are used instead. However, we could assume they are the same, both affected by Time, and that is why I think deSitter chose them to make his point concerning "Thinking in 4D".

In that case, I agree with deSitter, that additional dimension elements, or at least suitably altered dimensions (an abberation), are implied in the demonstrations. And we could agree that all of the aberrations are due to a change in the dimension of "Time" (aka the 4th dimension). In other words, we see only a time related dimensional change when "timing" changes. I would think the 4th dimension must(?) be present at all times, even in the absence of *apparent* motion. Could we not say, then, that whenever time alters (becomes a changing property of) any common 3 dimensions, we are considering a change of time to cause a corresponding dimensional appearance change of the 4th dimension, that of Time itself?

It is **almost** as if we, as humans, cannot really visualise true reality. we seem to be unable to stand off to the side as dis-interested neutral observers, since we are an integrated part of the swirling process. Can a grain of wheat ever know it will become bread? Yet we seek, and maybe we can find, an ever more neutral frame of rest from which to observe. After I have learned more, I have a complicated, yet simple "frame of rest" idea, that heavily depends on foreshortening, that we could all perhaps explore someday in another thread.

I think the main value of the "Thinking in 4D post" phenomena is the brilliant explanation of apparent superluminal observations, the most important result of such work. This is a real practical use, in astronomy, for properly thinking the effects through, that deSitter has presented. I urge everyone to read through that page link if they have not already done so.

To me, it was important to discover during the "Thinking in 4D" foray, that foreshortening is still "real", and still must occur, even though the visual concept may not be what I once expected.

## Faster than Light "Entanglement"

If you consider Physics and Relativity part of Astronomy (I do), you might be interested in this article. Physicist and science fiction writer John Cramer is going to try to get information going faster than the speed of light by splitting laser beams and coercing the waves into particles. And he's going to try to do this by Sept. 15. Pretty interesting, if you're into this stuff.

In case the article gets de-linked, click here for Prof. Cramer's website.

### #2 llanitedave

### #3 b1gred

The speed of light in fiber (sinble mode) is about 0.6C or 60% of the speed of light in a vacuum. Wonder if he's taken this into account? This will be fun to watch.

### #4 jamida

He's not doing a local speed of light (glass vs vacuum) experiment, he's doing a variation on the EPR experiment.

My physics degree is several years behind me, but it goes something like this. Entangle two photons, they'll have multiple independent properties that are related. Left vs right polarization and circular-right vs circular-left polarization for example. When you measure one of these **instantly** the other acquires the opposite value. The hidden variable thesis posits that this is no big thing as the photons were like dice tumbling in lock step with each other as they travel. So if we measure a die with a value of "2" then the other die has a value of "5" (maintaining a "7" total) it'd be wrong to jump to the conclusion of there being some instantaneous communication between the two dice/photons.

However, hidden variables has been shown to not be an explanation by Bell's inequality and related experiments.

This isn't strictly a violation of Einstein's speed limit as one can't use this effect to communicate information, but here is where my understanding of Cramer's experiment stops. he seems to be doing something that pushes this a little further.

### #5 HiggsBoson

I would consider Astronomy the experimental part of Astrophysics.

Clearly Astronomy is a sub-set of physics not the other way around. It is the process of taking data or making observations on the universe. As with the other areas of physics theoretical and experimental work must cooperate in order to make progress. Theory* is worthless without physical verification. Similarly, observation without theory gets you nowhere.

There are plenty of theories* without experimental support. Examples of observations without theory would include the photoelectric effect prior to 1905 and the speed of light prior to Special Relativity.

Theatrical Astrophysics was my major for my first two years in collage. I later changed to theoretical particle physics. 25 years later I suddenly got interested in telescopes. It never occurred to me to look through one while I was in school.

“Entanglement” is a very interesting topic but it is too far past my bed time for me to allow myself to start thinking about it. I suggest reading “The Fabric of the Cosmos” by Brian Green. Chapter 15 deals with teleporters and Time Machines.

* I use the word loosely. Technically a hypothesis is not promoted to a theory until there has been at least one successful experimental test.

## Is it possible to go faster than speed of light?

Expansion of the universe has happened faster than the speed of light.

And this is something that strains my understanding, like much of relativistic physics. Possibly inflation allowed that because space itself was expanding. I'm interested, but I probably won't comprehend the answers.

When you are accelerating in your car, the far reaches of the universe and the galaxies at that distance, are moving toward you much faster than the speed of light. They stop moving toward you when you stop accelerating.

### #27 FirstSight

For matter to travel faster than light, it would have to have not *negative* mass, but *imaginary* mass, which can only be described with imaginary (complex) numbers, i.e. numbers like a + b*i* where *i* = sqrt(-1).

. which is why faster-than-light travel by astronauts so far only exists in the *imaginary* space of science fiction.

### #28 fjh

For matter to travel faster than light, it would have to have not

negativemass, butimaginarymass, which can only be described with imaginary (complex) numbers, i.e. numbers like a + biwherei= sqrt(-1).

These are statements are about the GR mathematical model - not the universe. While they may very well be true about the universe as well, they may not. Just as Newtonian physics did not capture the whole story, GR may not capture it either.

### #29 fjh

### #30 fjh

### #31 PeterR280

Mathematical models are just that. They describe the universe with varying levels of accuracy. In some cases, the math blows up as in the case of a black hole and General Relativity.

Newtonian mechnics works very well until you reach strong gravitational fields or high velocities, Then, GR provides a more accurate prediction until you get to black holes or the expansion of the universe or gravitional behavior at the galactic level. A more accurate model is needed to describe those things but it will still be a model and not the actual universe.

### #32 GJJim

Mathematical models are just that. They describe the universe with varying levels of accuracy. In some cases, the math blows up as in the case of a black hole and General Relativity.

Newtonian mechnics works very well until you reach strong gravitational fields or high velocities, Then, GR provides a more accurate prediction until you get to black holes or the expansion of the universe or gravitional behavior at the galactic level. A more accurate model is needed to describe those things but it will still be a model and not the actual universe.

Only a model? Mass gives the universe scale and complexity. Its presence allows the processes of time and entropy. A universe with no matter, only photons, has no "size" or scale because a photon sees no passage of time. Whether it travels a Planck length or trillions of light years, the photon doesn't change. From what we observe and understand about thermodynamics, the universe of the distant past was in a state of near zero entropy (within 1/e^(10^123) according to Penrose). It was essentially a featureless void slightly warmer than absolute zero. If the only particles in this universe were photons, then this initial state was no different than a "mathematical model". Roger Penrose's book *Conformal Cyclic Cosmology* proposes a theory (and tests) for a universe that arises from a mathematical feasance (some might call it "nothing" or a model ) and evolves to the same.

### #33 PeterR280

Mathematical models are just that. They describe the universe with varying levels of accuracy. In some cases, the math blows up as in the case of a black hole and General Relativity.

Newtonian mechnics works very well until you reach strong gravitational fields or high velocities, Then, GR provides a more accurate prediction until you get to black holes or the expansion of the universe or gravitional behavior at the galactic level. A more accurate model is needed to describe those things but it will still be a model and not the actual universe.

Only a model? Mass gives the universe scale and complexity. Its presence allows the processes of time and entropy. A universe with no matter, only photons, has no "size" or scale because a photon sees no passage of time. Whether it travels a Planck length or trillions of light years, the photon doesn't change. From what we observe and understand about thermodynamics, the universe of the distant past was in a state of near zero entropy (within 1/e^(10^123) according to Penrose). It was essentially a featureless void slightly warmer than absolute zero. If the only particles in this universe were photons, then this initial state was no different than a "mathematical model". Roger Penrose's book *Conformal Cyclic Cosmology* proposes a theory (and tests) for a universe that arises from a mathematical feasance (some might call it "nothing" or a model ) and evolves to the same.

Mathematical models are constructs of the human mind.

### #34 GJJim

Only a model? Mass gives the universe scale and complexity. Its presence allows the processes of time and entropy. A universe with no matter, only photons, has no "size" or scale because a photon sees no passage of time. Whether it travels a Planck length or trillions of light years, the photon doesn't change. From what we observe and understand about thermodynamics, the universe of the distant past was in a state of near zero entropy (within 1/e^(10^123) according to Penrose). It was essentially a featureless void slightly warmer than absolute zero. If the only particles in this universe were photons, then this initial state was no different than a "mathematical model". Roger Penrose's book *Conformal Cyclic Cosmology* proposes a theory (and tests) for a universe that arises from a mathematical feasance (some might call it "nothing" or a model ) and evolves to the same.

Mathematical models are constructs of the human mind.

Which leads to a paradox first described by Karl Popper. How is it possible for the human mind, a physical construct existing in a physical universe, to intuit the mathematical schema which describe the universe -- unless -- those schema are *integral to the whole*? It can be argued that mathematical truth is the progenitor, the absolute origin, of what we call physical reality.

### #35 fjh

Which leads to a paradox first described by Karl Popper. How is it possible for the human mind, a physical construct existing in a physical universe, to intuit the mathematical schema which describe the universe -- unless -- those schema are *integral to the whole*? It can be argued that mathematical truth is the progenitor, the absolute origin, of what we call physical reality.

http://www.mountainl. el/3worldsx.jpg

[/quote]

Does this paradox have a name? If so, what is it called? Would you please provide a reference so I can learn some more?

### #36 llanitedave

Mathematical models are constructs of the human mind.

Which leads to a paradox first described by Karl Popper. How is it possible for the human mind, a physical construct existing in a physical universe, to intuit the mathematical schema which describe the universe -- unless -- those schema are *integral to the whole*? It can be argued that mathematical truth is the progenitor, the absolute origin, of what we call physical reality.

Does this paradox have a name? If so, what is it called? Would you please provide a reference so I can learn some more?

I don't remember whether Popper tried to actually resolve the paradox or not, but in the end, I don't think it's really necessary. The human mind is shaped by evolution, and natural selection is constrained by the existing physical reality which ancestral brains were forced to accommodate. Mathematics does not have to be "the origin", it only has to be integrated into the biological reality of the near-present. But continuity implies that if the processes operating on Earth in near time have a mathematical integrity, then that integrity is a reflection, or an embedded subset, of something broader and more universal. A capricious set of attributes at the origin is not beyond the bounds of credibility, but *since* that origin, continuity has held sway, which allows us to successfully project our reality-evolved logical/mathematical abilities towards the understanding of the cosmos as a whole.

Mathematical models may indeed be constructs of the human mind, but the human mind is a construct of a mathematically-consistent universe.

### #37 GJJim

*integral to the whole*? It can be argued that mathematical truth is the progenitor, the absolute origin, of what we call physical reality.

http://www.mountainl. el/3worldsx.jpg

[/quote]

Does this paradox have a name? If so, what is it called? Would you please provide a reference so I can learn some more?

The paradox has several expressions, Popper and Eccles looked at its implications for the concept of the human mind and free will. Other scientists (Penrose et al.) see it in terms of objective reality and universal truths extant the physical mind.

### #38 PeterR280

maybe we are living in a large computer program.

### #39 fjh

maybe we are living in a large computer program.

### #40 llanitedave

### #41 petrus45

I kind of liked EJN's description of a location "outside" the spacetime cone as being "imaginary." Imaginary, as I understand it in this context, means a concept the human mind has constructed based on sound reasoning, but which is nevertheless not "real." Another example would be that mathematics can describe the proposition x 2 = -1, even though there is no value you could find on a number line, that could satisfy x. But you can still get out a piece of paper, draw a line, put a zero in the middle, 1-10 on the right, negative 1-10 on the left, and then draw a point not on the line. It's possible to do that.

Similarly, the mind can construct a concept of something that goes faster than the speed of light, i.e. a point outside the spacetime cone graph, but that point by definition would not be "real".

However, I am not a mathematician, and want to take this a step further: How are "imaginary" mathematical propositions (like a speed faster than the speed of light) different from other "imaginary" thinks like unicorns? Why does mathematics not use the term "false" or "unproven" for those concepts? The term "imaginary" seems to confer a connotation of quasi-reality, i.e. "it exists in your mind" that is not present in things that are "false." For example, some posts are talking about the concept that the universe is a construct of our mind, and reciprocally that our mind is imprinted with the structure of the universe.

But what if our minds and the universe actually contain a design flaw, and we can cognitively "know" true information with 100% certitude, but the information can at the same time be imaginary and false? The implications are sort of troubling, but I'm sure I am conflating different concepts. Can someone straighten me out?

**Edited by petrus45, 06 February 2015 - 05:20 PM.**

### #42 GJJim

I kind of liked EJN's description of a location "outside" the spacetime cone as being "imaginary." Imaginary, as I understand it in this context, means a concept the human mind has constructed based on sound reasoning, but which is nevertheless not "real."

[. ]

However, I am not a mathematician, and want to take this a step further: How are "imaginary" mathematical propositions (like a speed faster than the speed of light) different from other "imaginary" thinks like unicorns? Why does mathematics not use the term "false" or "unproven" for those concepts?

In mathematics the proper label is *complex* numbers, but the term "imaginary" is often used. Complex numbers are useful tools that work in a variety of "real world" applications from electromagnetics to neurobiology. They are 100% legit and real.

### #43 petrus45

I kind of liked EJN's description of a location "outside" the spacetime cone as being "imaginary." Imaginary, as I understand it in this context, means a concept the human mind has constructed based on sound reasoning, but which is nevertheless not "real."

[. ]

However, I am not a mathematician, and want to take this a step further: How are "imaginary" mathematical propositions (like a speed faster than the speed of light) different from other "imaginary" thinks like unicorns? Why does mathematics not use the term "false" or "unproven" for those concepts?

In mathematics the proper label is *complex* numbers, but the term "imaginary" is often used. Complex numbers are useful tools that work in a variety of "real world" applications from electromagnetics to neurobiology. They are 100% legit and real.

Well, my understanding is that even complex numbers depend upon "assuming" the imaginary proposition that a value exists whereby x 2 =(-1), which would be false. Or, stated another way, the value of "x" is an imaginary value. But tech people nevertheless are able to take a leap of faith and use that as a bridge to get a practical answer that works in the real world. Sort of like when Indiana Jones walked over the invisible bridge to get from point A to point B, and find the Holy Grail.

But that still begs the question: What if the physical world with all of its properties - or maybe just our minds- are based on a "design flaw"? Seems like when you have to assume a proposition that is demonstrably false to derive results that are demonstrably true, that shows there is a problem.

**Edited by petrus45, 06 February 2015 - 08:55 PM.**

### #44 PeterR280

Complex numbers are routinely used in mathematics to solve real number problems. The first foray into number involving square roots of negative numbers came when solutions were formulated for cubic equations such as x3+ax+b=0. The cubic equation can have 3 real number solutions but the root calculations involve square roots of negative numbers. The imaginary numbers cancel each other out if all the roots are real.

In special relativity, a square of a length in 4-dimensional Minkowski space is written as s^2=c^2*t^2-x^2-y^2-z^2 (the more common form now. it can also be written as positive spacial dimensions and an imaginary time dimension) where the length equation implies that the dimensional values are imaginary.

In quantum mechanics, wave functions take the form e^ix, a complex number instead of sin(x). You need the imaginary components to solve the equations.

So complex numbers are used all the time in mathematics and it is viewed as a tool to solve problems.

**Edited by PeterR280, 06 February 2015 - 06:09 PM.**

### #45 fjh

My wife - in fact she bugs me and debugs me simultaneously!

And I remain happily married after 45 years.

### #46 llanitedave

I kind of liked EJN's description of a location "outside" the spacetime cone as being "imaginary." Imaginary, as I understand it in this context, means a concept the human mind has constructed based on sound reasoning, but which is nevertheless not "real." Another example would be that mathematics can describe the proposition x 2 = -1, even though there is no value you could find on a number line, that could satisfy x. But you can still get out a piece of paper, draw a line, put a zero in the middle, 1-10 on the right, negative 1-10 on the left, and then draw a point not on the line. It's possible to do that.

Similarly, the mind can construct a concept of something that goes faster than the speed of light, i.e. a point outside the spacetime cone graph, but that point by definition would not be "real".

However, I am not a mathematician, and want to take this a step further: How are "imaginary" mathematical propositions (like a speed faster than the speed of light) different from other "imaginary" thinks like unicorns? Why does mathematics not use the term "false" or "unproven" for those concepts? The term "imaginary" seems to confer a connotation of quasi-reality, i.e. "it exists in your mind" that is not present in things that are "false." For example, some posts are talking about the concept that the universe is a construct of our mind, and reciprocally that our mind is imprinted with the structure of the universe.

But what if our minds and the universe actually contain a design flaw, and we can cognitively "know" true information with 100% certitude, but the information can at the same time be imaginary and false? The implications are sort of troubling, but I'm sure I am conflating different concepts. Can someone straighten me out?

Two things. First, we can't know anything about the physical universe with 100% certitude. We can have clear and convincing proof that a certain assertion is *false*, but we can never know 100% if an alternative to it is *true*. That's because it takes far less information to falsify a proposition than to confirm it. The best way to approach truth, it seems, is by elimination of falsities, but there are always many more possible falsehoods than there are truths, so it's difficult to impossible to be assured you have found "the one and only."

Second, an imaginary concept in mathematics, such as a velocity faster than light, is qualitatively different than an imaginary concept in the world of experience, such as unicorns. An imaginary construction (as opposed to the imaginary unit) can be valid in mathematics if and only if it follows all valid mathematical rules and obeys the requisite mathematical logic. Even an imaginary mathematical object is constrained by the rules of mathematical logic. A classic example is the quadratic equation, which can provide two answers that are completely valid mathematically, both are "true" in that sense, but possibly only one of them is "real".

Unicorns, on the other hand, is an assertion about physical reality, not mathematical truth. We're not constrained by mathematical logic in the imagination of physical or biological objects. We're not even constrained by the laws of physics. Even where a creature is not inconsistent with physical laws, though, it's not likely *a priori* to exist. Only an infinitesimal fraction of the number of forms that are in principle evolutionarily possible have in fact appeared. Species of horselike creatures are all vanishingly unlikely in the sense of all the possible permutations of biological design space. There would be no reason to believe in the existence of a burro, or donkey, or zebra, or mule, or mustang if there were no physical evidence in the world to support the description of them. Once we gain more understanding of the relationships between different creatures, we become more able to explain, using logic akin to mathematical reasoning if not quite so rigorous, why a unicorn is a plausible example of a horselike organism or why it is not. And then we can look for evidence that will tend to confirm or falsify the idea.

That's the main difference between understanding the physical world and the mathematical world. Mathematics stands on its own in the use of logical rules -- if a proposition obeys those rules, then there's no reason why it shouldn't be valid. The physical world uses those same rules in an attempt to understand the relationships between observed behaviours of physical things, but the rules by themselves are not sufficient for understanding. One must also have those observations, those units of physical evidence.

### Faster Than Light Galaxies? WHAT.

Post by **smeyer8015** » Fri Dec 11, 2020 11:25 pm

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### Re: Faster Than Light Galaxies? WHAT.

Post by **Graeme1858** » Sat Dec 12, 2020 9:07 am

So what is Peculiar Velocity?

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### Re: Faster Than Light Galaxies? WHAT.

Post by **notFritzArgelander** » Sat Dec 12, 2020 3:36 pm

Graeme1858 wrote: ↑ Sat Dec 12, 2020 9:07 am So what is Peculiar Velocity?

It is the velocity peculiar to an individual galaxy or object apart from the overall velocity or flow. So in this case it is the individual velocity of the Earth or a galaxy with respect to the CMB.

A simple terrestrial example is a flock of migrating geese. The flock has an overall velocity. When geese change position in the V formation they do so through a peculiar velocity difference from the overall flock velocity. (The position at the apex of the V is tiring for the lead goose. The following geese get an extra boost from the wake of geese ahead in the formation. So the flock cooperatively rotates positions in the V.)