Undergrad Understanding Relativity: How Moving Objects Experience Near Light Speed Travel

[PeroK]

This is wrong, because of relativity. The assumed speed of the spaceship makes the low energy photons hard (see the Wikipedia quote above). If we can even measure the bow wave of solar winds at the boundary of the heliosphere, then CMB definitely becomes an issue at near c speeds. But again: I provided the contact data of the person who made this claim. Send an email and ask the theoretical physicist who made this claim. If I had to choose whom I trust more ...

This IS wrong. The CMB has a typical frequency of $1.6 \times 10^{11} \ Hz$. Hard gamma rays have a frequency of about $1.6 \times 10^{19} \ Hz$. That requires a gamma factor of about $10^8$ or a speed of $(1 - \epsilon)c$, where $\epsilon \approx 10^{-16}$.

The speed quoted by @DrStupid above, would boost the CMB to UV light - subject to checking that calculation.

 

[fresh_42]

This IS wrong. The CMB has a typical frequency of $1.6 \times 10^{11} \ Hz$. Hard gamma rays have a frequency of about $1.6 \times 10^{19} \ Hz$. That requires a gamma factor of about $10^8$ or a speed of $(1 - \epsilon)c$, where $\epsilon \approx 10^{-16}$.

The speed quoted by @DrStupid above, would boost the CMB to UV light - subject to checking that calculation.

Guess British (see quotation above) and German (see quotation above) universities are all wrong then and some guys on the internet are right. I have quoted two sources (one if we omit Wikipedia) that CMB is a source for inverse Compton scattering. Where is your proof it is not?

 

[PeroK]

Guess British (see quotation above) and German (see quotation above) universities are all wrong then and some guys on the internet are right. I have quoted two sources (one if we omit Wikipedia) that CMB is a source for inverse Compton scattering. Where is your proof it is not?

Inverse Compton scattering is not particularly relevant for the limitations on spaceship travel. Your lack of knowledge and your pop-science source are leading you astray here.

Stay calm and learn some physics!

 

[fresh_42]

Inverse Compton scattering is not particularly relevant for the limitations on spaceship travel. Your lack of knowledge and your pop-science source are leading you astray here.

Stay calm and learn some physics!

Stay calm and learn some physics!

Do you really want to discuss on an ad hominem level? Well, I'm ready to do so. I think you should publish your knowledge then, if British and German professional astronomers teach it all wrong.

 

[fresh_42]

5 Joule are necessary to scatter CMB.
https://cds.cern.ch/record/384407/files/9904108.pdf (p.35)

 

[fresh_42]

Inverse Compton scattering is not particularly relevant for the limitations on spaceship travel.

Near speed of light? Where is your evidence for that claim? And some hand wavy numbers do not count. They are worth even less than pop science.

 

[DrStupid]

The assumed speed of the spaceship makes the low energy photons hard (see the Wikipedia quote above).

I read the quote and didn't find enything that supports your claim.

If we can even measure the bow wave of solar winds at the boundary of the heliosphere, then CMB definitely becomes an issue at near c speeds.

That depends on the definition of "near c speeds". At least 0.999999991 c is nowhere near the limit you are talking about.

I provided the contact data of the person who made this claim.

I watched the video and didn't find enything that supports your claim.

 

[fresh_42]

I watched the video and didn't find enything that supports your claim.

Seen, but probably not understood.
0:10
3:50
5:00
5:30-6:30
etc.

 

[weirdoguy]

If I had to choose whom I trust more ...

The most important thing that PF tought me is that you can't trust pop-sci sources, no matter who is talking. Even Hawking wrote dobious stuff in his pop-sci books. I would've expected that Mentors know this...

 

[fresh_42]

The most important thing that PF tought me is that you can't trust pop-sci sources, no matter who is talking. Even Hawking wrote dobious stuff in his pop-sci books. I would've expected that Mentors know this...

I cited a total of 4 sources, 2 of them scientific sources, one an ordinary professor.

And I haven't seen a single reference that they are all wrong. Those who can read have a clear advantage. Sorry, but I really doubt that a spaceship can be accelerated close to c without providing more energy to its own electrons than 5 Joule. However, I would appreciate to see such a calculation. Maybe in the science jokes forum?

 

[PeroK]

Sorry, but I really doubt that a spaceship can be accelerated close to c without providing more energy to its own electrons than 5 Joule. However, I would appreciate to see such a calculation. Maybe in the science jokes forum?

$5J$ is a lot of energy for an electron.

 

[DrStupid]

Seen, but probably not understood.

You or me?

0:10 - SRT supports interstellar (or even intergalactic) space travel by time dilation and length contraction
3:50 - about CMB
5:00 - blueshift of CMB in front of the ship
5:30-6:30 - pair production if energy is high enough (example: ultra-high-energy cosmic rays)

I still do not see how that supports your claim.

 

[fresh_42]

$5J$ is a lot of energy for an electron.

An entire spaceship accelerated to say .8c, too. The spaceship itself becomes a cosmic ray, not the CMB. This blue shifts to X-ray frequencies. Both together are enough scattering energy for particle production.

 

[fresh_42]

You or me?

0:10 - SRT supports interstellar (or even intergalactic) space travel by time dilation and length contraction
3:50 - about CMB
5:00 - blueshift of CMB in front of the ship
5:30-6:30 - pair production if energy is high enough (example: ultra-high-energy cosmic rays)

I still do not see how that supports your claim.

I'm happy that CERN does. Still better than some guys on the internet. This is getting ridiculous. I want to see the proof of your statement: "CMB is irrelevant for a rocket accelerated to say 0.8c"

 

[vanhees71]

This is wrong, because of relativity. The assumed speed of the spaceship makes the low energy photons hard (see the Wikipedia quote above). If we can even measure the bow wave of solar winds at the boundary of the heliosphere, then CMB definitely becomes an issue at near c speeds. But again: I provided the contact data of the person who made this claim. Send an email and ask the theoretical physicist who made this claim. If I had to choose whom I trust more ...

Sure, if you travel with a speed $v=\beta c$ relative to the restframe of the CMBR the CMBR em. waves propagating directly against the direction of $v$ lead to the (maximal) blue shift of
$$\omega'=\sqrt{\frac{1+\beta}{1-\beta}} \omega.$$
In fact in this direction you observe a black-body spectrum with the correspondingly higher "effective temperature"
$$T_{\text{eff}}'=\sqrt{\frac{1+\beta}{1-\beta}} T,$$
where $T$ is the proper invariant (scalar) temperature measured by a thermometer in the CMBR rest frame. If $\beta \rightarrow 1$ you get arbitrary high temperatures leading to a blue shift of the CMBR to any hard-$\gamma$-ray range you like.

[EDIT: To clarify in view of #46] Of course the quantities with primes refer to what's observed in the space ship's restframe and the unprimed ones refer to the CMBR restframe.

 

[PeterDonis]

The spaceship itself becomes a cosmic ray, not the CMB. This blue shifts to X-ray frequencies. Both together are enough scattering energy for particle production.

You're double counting here. You can't blueshift the CMB and also treat the spaceship itself as a cosmic ray. If you are blueshifting the CMB, then you are working in the spaceship's rest frame, which means the spaceship's kinetic energy is zero. Or if you call the spaceship a cosmic ray, then you are working in the CMB rest frame, which means the CMB temperature is 2.7 K. You have to pick one; you can't take the higher energy value from both.

 

[PeroK]

An entire spaceship accelerated to say .8c, too. The spaceship itself becomes a cosmic ray, not the CMB. This blue shifts to X-ray frequencies. Both together are enough scattering energy for particle production.

$0.8c$ relative to the comoving frame is not, however, a barrier which a spacecraft could not possibly overcome.

 

[fresh_42]

You're double counting here. You can't blueshift the CMB and also treat the spaceship itself as a cosmic ray. If you are blueshifting the CMB, then you are working in the spaceship's rest frame, which means the spaceship's kinetic energy is zero. Or if you call the spaceship a cosmic ray, then you are working in the CMB rest frame, which means the CMB temperature is 2.7 K. You have to pick one; you can't take the higher energy value from both.

Yeah, that's true. Let's take the protons then. The question remains: How far can we accelerate a massive object before inverse Compton scattering from CMB becomes an issue? My claim is, long before .8c, others say it's irrelevant. CERN says 5 Joule are necessary to start the process. The cosmological background is that we observed hard cosmic rays scattering at CMB. Is there any reason a rocket would make an exception?

 

[fresh_42]

$0.8c$ relative to the CMB is not, however, a barrier which a spacecraft could not possibly overcome.

The hypothesis is, that energy invested in acceleration will be consumed by the production of pions at some stage, and thus not available anymore for further acceleration. The question can only be: where is that barrier? If Lesch is right and there are 400 photons CMB in every cubic centimeter of space, then I only claim that this is enough to become an issue long before c.

 

[DrStupid]

I'm happy that CERN does.

Provide a proper reference.

I want to see the proof of your statement: "CMB is irrelevant for a rocket accelerated to say 0.8c"

Just do the math. With

$\beta = 1 - \varepsilon$

blueshift is

$f' = f \cdot \sqrt {\frac{{1 + \beta }}{{1 - \beta }}} = f \cdot \sqrt {\frac{2}{\varepsilon } - 1} \approx f \cdot \sqrt {\frac{2}{\varepsilon }}$

The maximum of the CMB is at 282 GHz and 0.8 c corresponds to $\varepsilon = 0.2$. That results in 846 GHz for the maximum of the blueshifted CMB. That means we are talking about IR radiation corresponding to a temperature of 8.6 K. How is that relevant for a rocket?

 

[fresh_42]

Provide a proper reference.

What do you expect? Shall I read it for you? I gave a proper link and the page.

 

[fresh_42]

Just do the math. With

$\beta = 1 - \varepsilon$

blueshift is

$f' = f \cdot \sqrt {\frac{{1 + \beta }}{{1 - \beta }}} = f \cdot \sqrt {\frac{2}{\varepsilon } - 1} \approx f \cdot \sqrt {\frac{2}{\varepsilon }}$

The maximum of the CMB is at 282 GHz and 0.8 c corresponds to $\varepsilon = 0.2$. That results in 846 GHz for the maximum of the blueshifted CMB. That means we are talking about IR radiation corresponding to a temperature of 8.6 K. How is that relevant for a rocket?

The rocket is the issue. We have low energy photons and high energy electrons and protons in that collision.

 

[PeterDonis]

5 Joule are necessary to scatter CMB.

5 Joules per particle. Not 5 Joules total. Big difference.

 

[fresh_42]

5 Joules per particle. Not 5 Joules total. Big difference.

Yes. And protons. How fast do they have to be to pass 5J?

 

[PeterDonis]

The rocket is the issue. We have low energy photons and high energy electrons and protons in that collision.

But in the rocket rest frame we have low energy electrons and protons and high energy photons. Both frames must give the same answer. And other people are making what look to me like reasonable calculations in the rocket rest frame that say that, for example, at 0.8 c, the CMB looks like infrared radiation--i.e., the kind of stuff that is everywhere in our normal Earth environment and doesn't cause problems for ordinary objects, including spaceships. So I don't think this is such a slam dunk in your favor that you can just dismiss the objections that are being made.

 

[PeroK]

Yes. And protons. How fast do they have to be to pass 5J?

See:
https://en.wikipedia.org/wiki/Ultra-high-energy_cosmic_ray

Many orders of magnitude closer to the speed of light than you've been claiming.

 

[PeterDonis]

And protons. How fast do they have to be to pass 5J?

Proton rest mass 936 MeV, or about $10^9$ eV. 5 J = about $10^{19}$ eV. So gamma factor of about $10^{10}$.

 

[fresh_42]

Proton rest mass 936 MeV, or about $10^9$ eV. 5 J = about $10^{19}$ eV. So gamma factor of about $10^{10}$.

Inverse Compton was my guess. Lesch argued that we had observed particle scattering at CMB. Given that, the only question remaining is: at which rocket speed? The point is that the energy we have to invest in acceleration grows dramatically, too, and thus there will not be enough energy available once particles are created.

 

[vanhees71]

Of course not. In the reference frame of the spaceship, moving fast enough wrt. the CMBR restframe, there can be CMBR photons, but you need much higher speeds than 0.8 c.

The maximum of the black-body spectrum is at frequencies of
$\nu \simeq T 6 \cdot 10^10 \text{Hz}/\text{K}.$
The threshold for pair production is at photon energies of $2 m_{\text{e}} \simeq 1 \text{MeV}$. The corresponding frequency is $\nu=1 \text{MeV}/h \simeq 1.6 \cdot 10^{-16} \text{J}/h \simeq 2.4\cdot 10^{17} \; \text{Hz}$. The temperature where this is at the maximum of the Planck distribution thus is $T \simeq 4 \cdot 10^6 \; \text{K}$.

Now the CMBR proper temperature is about $2.75 \text{K}$, i.e., you'd need a blueshift factor of $\sqrt{(1+\beta)/(1-\beta)} \simeq 1.47$. This gives $\beta \simeq 1-9.3 \cdot 10^{-13}$ ;-).

I hope, I typed everything correctly in my pocket calculator ;-).

 

[PeroK]

Inverse Compton was my guess. Lesch argued that we had observed particle scattering at CMB. Given that, the only question remaining is: at which rocket speed? The point is that the energy we have to invest in acceleration grows dramatically, too, and thus there will not be enough energy available once particles are created.

Yes, but as has been repeatedly pointed out, this doesn't stop you getting to Andromeda in about 28 years, for example.

The effects that Lesch is talking about are a) not at speeds that would hinder relativistic space travel; and, b) at speeds where the spacecraft would long since have melted in any case!

There is a case that free particles are eventually slowed below a given threshold relative to the CMB. The distance given was 50 Mpc in the paper you quoted.

Whether this cosmic-ray-speed-limit applies to theoretical space travel is a moot point. But, in any case, a) and b) above apply.