# Light speed versus very Very VERY near Light speed.

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#### Solifugae

##### Guest
Mathematically, things such as mass, and time dilation factor become infinite at the speed of light.
In a relativistic ship, your personal time could be mere minutes for a journey that takes you across four light years from the frame of earth observers. As your speed comes closer and closer to that of light, it could be mere seconds. AT lightspeed it should be zero. This brings up the strange concept of "the point of view of a photon". Traveling at the speed of light would mean ZERO personal time, and therefore it would be impossible for any processes to actually occur. You'd be frozen. You would reach absolute zero for one thing. The frozen time resembles the nature of black holes in a way. Isn't it true that an object with rest mass going at the speed of light would BECOME a black hole? Its mass would be infinite after all. So, it's not just the lack of infinite power preventing light speed travel. The sheer logistics of it do not seem to work.

However, my question is: could an object with mass be SO close to the speed of light that its speed cannot be measured to be any different than that of light? How fast would this be? I know we have determined cosmic rays that would be only nanometers behind light after traveling a light year (The Oh-my-god particle?).

Something I'm wondering about here is the nature of the quantum universe and how it affects this. There are things we cannot measure, things below the Planck units for example where quanta and probability take over.
Let's say that something was 1 Planck length slower than light over a distance of the observable universe. It's speed would be indistinguishable from that of light, because it cannot be measured to be any different. However, would it be functionally equivalent to light? The energy required to accelerate this particle to that speed would not be infinity, it would just be absurdly high. None of its values should be infinity. Yet, in practice, its values may not be measurable to be any different. Is it possible that light itself has merely this speed?

Is this possible, or am I misunderstanding things?

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#### aphh

##### Guest
What governs lightspeed actually? We can measure and calculate the speed of light in different mediums, but do we know why the speed of light is what it is?

Of the electromagnetic spectrum light isn't even the shortest wavelength specie.

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#### ramparts

##### Guest
aphh":3t7rlb3p said:
What governs lightspeed actually? We can measure and calculate the speed of light in different mediums, but do we know why the speed of light is what it is?

Of the electromagnetic spectrum light isn't even the shortest wavelength specie.

The speed of light is a speed that's fundamental to the universe - it's sort of "engrained", literally, in the fabric of spacetime. It's the speed at which all massless particles - including photons, the carriers of light - travel.

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#### aphh

##### Guest
Sure, but it doesn't answer the question. Again, what governs lightspeed?

What made lightspeed to be the speed that light has? I can understand the speed of sound being governed by the physical media in which the soundwaves propagate.

However, in the emptiness of space there is no medium to govern the speed of light, so the speed must come from the propagation of the energy itself. But why does lightspeed have the value it has and not some other value?

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#### MeteorWayne

##### Guest
It is just a fundemental property of the Universe. There's really no why, it just is the way things work.

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#### aphh

##### Guest
What if lightspeed is governed by Dark Energy or Dark Matter? Surely there is something that governs it and puts a limit on it.

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#### MeteorWayne

##### Guest
Not necessarily. It seems just to be a constant in our Universe. If you can provide a mechanism where dark energy or dark matter is related, you can win a Nobel Prize. No one has even suggested such a connection that I am aware of.

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#### ramparts

##### Guest
aphh":2pfxtqfw said:
What if lightspeed is governed by Dark Energy or Dark Matter? Surely there is something that governs it and puts a limit on it.

Why does it need to be "governed"? Surely there's something which just is. Maybe it's the speed of light, maybe it's whatever determines (or "governs") the speed of light, but if you say something has to govern the speed of light, then you're forced into saying that something has to govern that first something, and so on and so forth - it brings you to weird places.

Why it has the exact value it does (2.99 * 10^8 m/s or somesuch) is something to which there is no answer. As MW said, if there is one, that's a Nobel-worthy achievement, easy. (almost as Nobel-worthy as inspiring hope)

Also, there's no reason at all to think that dark energy or dark matter have anything to do with it. Just because they're exciting and unknown fields of research doesn't mean they're the answer to all of the problems of physics.

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#### aphh

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ramparts":1sqbahkp said:
Why it has the exact value it does (2.99 * 10^8 m/s or somesuch) is something to which there is no answer.

There is no answer but something governed the speed of light to be 2.99 * 10^8 or somesuch, not 1.55 * 10^8 or 5.99 * 10^8, let alone something else.

What is it that governs the speed of light to be what it is? This is a fundamental question, not something to be taken lightly just "because it is what it is". Before Galileo and Newton came up with answers, objects fell to the ground "just because they fall to the ground. They do that, you know".

Most likely what governs the speed of light governs also space-time and gravity. If we learned more about the phenomena behind all this, we might be able to manipulate space-time for our advantage.

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#### SpacexULA

##### Guest
aphh":vffcanj4 said:
What is it that governs the speed of light to be what it is? This is a fundamental question, not something to be taken lightly just "because it is what it is". Before Galileo and Newton came up with answers, objects fell to the ground "just because they fall to the ground. They do that, you know".

Most likely what governs the speed of light governs also space-time and gravity. If we learned more about the phenomena behind all this, we might be able to manipulate space-time for our advantage.

That's the beautiful think about the scientific perspective. I can say "Hell if I know", and "Don't know yet, why don't you go investigate that", without feeling any remorse whatsoever.

We will know eventually, nature is a fickle witch, but we will get all the secrets out of her eventually. Maybe tomorrow, maybe in a thousand years. Religion guesses, Science researches.

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#### ramparts

##### Guest
aphh":151686r1 said:
ramparts":151686r1 said:
Why it has the exact value it does (2.99 * 10^8 m/s or somesuch) is something to which there is no answer.

There is no answer but something governed the speed of light to be 2.99 * 10^8 or somesuch, not 1.55 * 10^8 or 5.99 * 10^8, let alone something else.

What is it that governs the speed of light to be what it is? This is a fundamental question, not something to be taken lightly just "because it is what it is". Before Galileo and Newton came up with answers, objects fell to the ground "just because they fall to the ground. They do that, you know".

Most likely what governs the speed of light governs also space-time and gravity. If we learned more about the phenomena behind all this, we might be able to manipulate space-time for our advantage.

You seem to be missing my point. Yes, there might be something governing the value of c, and (as the above poster said) it's perfectly valid scientifically to say "I don't know what the answer is/if there's an answer, but we'll go do everything we can to find out." I am emphatically not saying there's no answer to your question and that we shouldn't look. What I am saying is that there doesn't have to be an answer of the kind you're suggesting.

Here's what I ask you: let's say some mysterious process which we don't understand yet governs the speed of light. That process needs to be governed too, by your logic. So what governs that? And then that governor of the governor - what governs that? Is everything governed by something else, ad infinitum, or does there have to be something which just is? I think philosophically the only logical answer is the latter (that something just is), and the speed of light may or may not be such a thing. In fact, I think it's probable that the speed of light is such a thing. If its value is determined, then it's determined by some other fundamental constant, so is it really that much better if the speed of light is "governed" but some other fundamental constant isn't?

A note: according to certain unified theories (in particular, string theory) there is a landscape of different universes, each of which have different values of the fundamental constants. That would answer your question (though it's not the most satisfying response): there's nothing "governing" c, it has randomized values depending on which universe you're in, and the universe we happen to be in has this particular value of c.

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#### Shpaget

##### Guest
Solifugae":82k6yj0h said:
Let's say that something was 1 Planck length slower than light over a distance of the observable universe. It's speed would be indistinguishable from that of light, because it cannot be measured to be any different. However, would it be functionally equivalent to light? The energy required to accelerate this particle to that speed would not be infinity, it would just be absurdly high. None of its values should be infinity. Yet, in practice, its values may not be measurable to be any different. Is it possible that light itself has merely this speed?

Is this possible, or am I misunderstanding things?

Let's say a bag of potatoes has mass of almost, but not exactly 1 kg. How close it has has to come to the actual 1 kg for the supermarket to be able to charge you one full kilogram?
Well, it depends on the type and accuracy of the scale they're using, doesn't it? One more thing is necessary to charge you almost but not exactly one full kg of those potatoes: the currency that is used to pay it for needs to be dividable (is that a word?) to adequately small fractions.
Tell me, if something has the price of \$99,99 would you expect the return of that one cent? Maybe.
But what if mathematically calculated price is actually 99,9999? What then? US dollars don't have \$0,0001 coins... Wouldn't it be reasonable to say the price is equal to \$100,00, even though it's not?

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#### Solifugae

##### Guest
I can see nothing yet to contradict the possibility that light has values extremely close to, but not equal to "mathematical c". Well, I don't see anything supporting it either, since if we could measure this, then we would already know it.

Hypothetically speaking, what would it mean for our universe if the speed of light did not reflect infinite values? Would this mean anything for black holes, for example? What about the cosmos at large? First of all, it would mean that with sufficiently absurd amounts of energy, a particle with mass could reach the speed of light, that's for sure. Even if we couldn't measure the difference between "real c" and our imaginary "mathematical c", could we infer it from the way this would effect the universe in general?

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#### ramparts

##### Guest
Solifugae":20hminem said:
I can see nothing yet to contradict the possibility that light has values extremely close to, but not equal to "mathematical c". Well, I don't see anything supporting it either, since if we could measure this, then we would already know it.

I don't think you can contradict that because such a thing as "mathematical c" doesn't exist. We don't derive c mathematically - we empirically test it.

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#### Solifugae

##### Guest
I'm not saying that we derive the actual speed of light through maths. Obviously, we measure it.

What I'm calling "mathematical c" here is the result of the theory of relativity applied to the measured speed of light, which takes values to infinity at c. For example, you need infinite energy to accelerate a body to c. It will then have infinite mass. It's time relative to other times will be infinitely slower.

However, if light was unmeasurably slower than our precision measured figures, these factors would not be infinity. They would merely be ridiculously large. This sounds untestable, since by definition, we wouldn't be able to test it. Wouldn't we be able to infer the effect of this on the universe though?

Using the example from before: what if light was 1 Planck length slower than the maximum accuracy to which we measure c over the length of the entire observable universe? From this angle: unlike what we think of light, photons do have rest mass and accelerate, it's just that they have such low mass and such quick acceleration that it is not measurable directly.

If light was the tiniest tiniest tiniest fraction slower than we think it is, what sort of effect would this have on the universe. Would some observed phenomena be impossible? If so, this implies that the mathematics of c are utterly correct when it comes to relativity. Indeed the "personal time" of a photon is zero.

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#### ramparts

##### Guest
Solifugae":na1vzdoh said:
I'm not saying that we derive the actual speed of light through maths. Obviously, we measure it.

What I'm calling "mathematical c" here is the result of the theory of relativity applied to the measured speed of light, which takes values to infinity at c. For example, you need infinite energy to accelerate a body to c. It will then have infinite mass. It's time relative to other times will be infinitely slower.

However, if light was unmeasurably slower than our precision measured figures, these factors would not be infinity. They would merely be ridiculously large. This sounds untestable, since by definition, we wouldn't be able to test it. Wouldn't we be able to infer the effect of this on the universe though?

It's not just untestable, it's unphysical. I mean, what you call "mathematical c" is a value that we put into relativity. It isn't a "result" of it. There is a speed with many different properties (the most famous one being that nothing can travel faster than it, but also that it is the same in all reference frames, requires infinite energy or zero mass to reach, is the dimensional constant converting between time and space dimensions, etc.) that we call c which goes into the theories of special and general relativity. It's pretty much defined as the speed of light, so your question more or less boils down to: what if light were slightly slower than what we measure it to be? Um, in that case, "mathematical c" would change as well

Of course, there is always another layer of detail to the answer. The fundamental speed which we call the speed of light isn't necessarily the speed of light. It's the speed of any massless particles. If photons had mass, they would travel slightly less than c - and nothing at all about relativity would be changed. I should also note that there's absolutely no reason, to the best of my knowledge, in any theory out there for light to have any value for mass even a tiny bit greater than 0 (in particular, it would require the breaking of symmetries which aren't broken in any currently viable physics model). That would mean that light would have no choice but to travel at c.

Using the example from before: what if light was 1 Planck length slower than the maximum accuracy to which we measure c over the length of the entire observable universe? From this angle: unlike what we think of light, photons do have rest mass and accelerate, it's just that they have such low mass and such quick acceleration that it is not measurable directly.

If light was the tiniest tiniest tiniest fraction slower than we think it is, what sort of effect would this have on the universe. Would some observed phenomena be impossible? If so, this implies that the mathematics of c are utterly correct when it comes to relativity. Indeed the "personal time" of a photon is zero.

Ah. As I said above.... no. If the photon has a non-zero mass that small, then it probably wouldn't be measurable - but there are also likely to be very good reasons why such masses are impossible. And no, again, if photons had mass, this would really have no effect on the universe, except that light would go a little slower than we expect. c wouldn't change, its role in relativity wouldn't change, and fundamental physics would be unchanged.

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#### Solifugae

##### Guest
So, where are the infinites derived from in relativity? I guess I need to understand that first.

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#### Solifugae

##### Guest
I don't see why that leads to infinities.

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#### ramparts

##### Guest
Which infinities? The idea that you need "infinite energy" to travel at the speed of light?

Well, think of it like this: As you move faster, you gain kinetic energy (proportional to mv^2). By E=mc^2, you can think of this extra energy as increasing your mass, so if there's some constant force accelerating you, then as you go faster, the m in F=ma increases, so a decreases. The limit of the velocity you can reach is the speed of light. In order to be accelerating to that speed, you need infinite force.

Another important infinity: there is a number called the Lorentz factor, which parametrizes your speed relative to the speed of light (the exact formula is 1/sqrt{1-v^2/c^2}). If your speed is 0, the Lorentz factor is one, and the faster you go, the higher the Lorentz factor, and at v=c it becomes infinite (1/0). The Lorentz factor is very important because pretty much any relativistic correction is based almost exclusively on that - for example, in length contraction, you just divide an object's length by the Lorentz factor to see how small it gets relativistically. Time dilation (how much slower time "ticks" when you move fast) is given by time multipled by the Lorentz factor. Relativistic energy is rest energy times the Lorentz factor. You can see how when the Lorentz factor goes to infinity, lots of things get screwed up.

Remember that in, for example, the Lorentz factor, the "c" we use is by definition the speed at which a massless particle (as we believe the photon to be) travels. So asking what happens if the speed of a massless particle were different is a meaningless question.q

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#### yevaud

##### Guest
Sorry; the prior post of mine was of general interest to the OP, not in answer to Solifugae's question about infinities.

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#### Solifugae

##### Guest
Well, think of it like this: As you move faster, you gain kinetic energy (proportional to mv^2). By E=mc^2, you can think of this extra energy as increasing your mass, so if there's some constant force accelerating you, then as you go faster, the m in F=ma increases, so a decreases. The limit of the velocity you can reach is the speed of light. In order to be accelerating to that speed, you need infinite force.

I understand the first bit, but I don't know where this factor increases the force needed to infinity.
I still don't get what proves that it would be infinite, rather than arbitrarily large. The smallest fraction away from the lightspeed you could have, it's just a massive effect, but then as soon as it goes to lightspeed it just jumps to infinity?

If you have values increasing exponentially towards a set point, they should still just reach a real number.

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#### yevaud

##### Guest
Solifugae":g6s7dv4v said:
If you have values increasing exponentially towards a set point, they should still just reach a real number.

No, think of an asymptote, where one continually grows infinitesimally closer and closer to the target, but never actually achieves it. One grows closer and closer to C, as in 99.9% C, 99.99% C, 99.999% C, etc., but the actual target of C is unachievable.

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#### ramparts

##### Guest
Exactly. Putting what yevaud said in terms of my last post, if the force F has a certain strength, you might be able to reach 99% of c. If you make the force stronger, maybe you can get to 99.9% of c. If you make the force even stronger, then you can maybe get to 99.99% of c, and so on. The stronger the force, the faster you can get, but no matter how strong the force you'll never actually get to c. That's what we mean by infinite force - no finite (or "real" as you call it in your post) force can reach c, but they can get arbitrarily close.

One possible problem: you say "it just jumps to infinity". When things asymptote (as in this case) they don't "jump" to infinity, they get arbitrarily large as you reach a certain value. Think of the function 1/x. If you set x equal to something very very small but just above 0 (like 0.000001) and plug it into 1/x, you'll get an enormous number. The smaller you make x, the larger 1/x becomes, but once you hit x=0, you can't calculate 1/x, it's infinite. Try plugging some values of x into your calculator and calculating 1/x, you'll see what I mean

Now let's say you plotted 1/x:

http://www.wolframalpha.com/input/?i=1%2Fx

Start at x=1 and start moving to the right along the curve. When x=1, you're at the height 1 (1/1=1). If you move along the curve a bit, you can get to x=0.5, where the height of the curve is 2 (1/0.5 = 2). But no matter what you do, you can never get to x=0. Think about how this relates to the issues you're having with c (hint: I'm trying to draw a loose analogy between x=0 and the speed of light).

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#### Solifugae

##### Guest
yevaud":sgi6pldc said:
No, think of an asymptote, where one continually grows infinitesimally closer and closer to the target, but never actually achieves it. One grows closer and closer to C, as in 99.9% C, 99.99% C, 99.999% C, etc., but the actual target of C is unachievable.

I understand what you're saying, but how do we know it works this way? What experiment showed us that the gradiant to c works this way? I know that relativity has been outright proven, but what in particular demonstrates that it is an asymptote and will result in infinity at c? Or maybe it is a theoretical requirement that must fit, rather than an experimental one? To use what rampart said about x=0, I understand that it does equal 0 at c, but not why we have set it to be zero at c. There must be something that showed this was the case.

It could still be harder and harder reach something and yet be able to reach it in the end. For example: You want to reach 100, using a numbered value that increases the actual number. At the start, let's say you need 1a to raise the number by 1, but the requirement goes up an order of magnitude, so you need 10a to raise the number to 2, and so on. To actually reach 100, you need something like 10^10x10a (I think), not an infinite amount of a. Relativity must be very very different from this example.

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